Transcript The ordinary arithmetic average of the set of numbers.

MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
8 appears more often (4 times)
than any other number.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
8 appears more often (4 times)
than any other number.
The mode is 8.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 2 numbers appear equally frequently, we’ll call both of them modes.
For a case like this, we say that the set of numbers is bimodal.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 2 numbers appear equally frequently, we’ll call both of them modes.
For a case like this, we say that the set of numbers is bimodal.
Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 2 numbers appear equally frequently, we’ll call both of them modes.
For a case like this, we say that the set of numbers is bimodal.
Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2
2 and 7 are tied (at 3 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 2 numbers appear equally frequently, we’ll call both of them modes.
For a case like this, we say that the set of numbers is bimodal.
Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2
2 and 7 are tied (at 3 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 2 numbers appear equally frequently, we’ll call both of them modes.
For a case like this, we say that the set of numbers is bimodal.
Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2
2 and 7 are tied (at 3 times) for the
most frequent number in the list.
The modes are 2 and 7.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
2, 3 and 5 are tied (at 2 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
2, 3 and 5 are tied (at 2 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
2, 3 and 5 are tied (at 2 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
2, 3 and 5 are tied (at 2 times) for the
most frequent number in the list.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MODE: The most frequent number in the set of numbers.
If 3 or more numbers appear equally frequently,
we will just agree to say that there is no mode.
Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3
2, 3 and 5 are tied (at 2 times) for the
most frequent number in the list.
There is no mode.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
The simplest way to find the median is
to put the numbers in order.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
The simplest way to find the median is
to put the numbers in order.
From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
The simplest way to find the median is
to put the numbers in order.
From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8
The middle number is 5.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
The simplest way to find the median is
to put the numbers in order.
From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8
The middle number is 5.
The median is 5.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
WhenFor
this any
happens
the𝑛median
is defined
set of
numbers
to be the average of the 2 middle numbers.
𝑥51+, 𝑥82 , 𝑥13
3 … , 𝑥𝑛
=
= 6.5
There are 3 common2measures
of central tendency.
2
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
WhenFor
this any
happens
the𝑛median
is defined
set of
numbers
to be the average of the 2 middle numbers.
𝑥51+, 𝑥82 , 𝑥13
3 … , 𝑥𝑛
=
= 6.5
There are 3 common2measures
of central tendency.
2
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
WhenFor
this any
happens
the𝑛median
is defined
set of
numbers
to be the average of the 2 middle numbers.
𝑥51+, 𝑥82 , 𝑥13
3 … , 𝑥𝑛
=
= 6.5
There are 3 common2measures
of central tendency.
2
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
WhenFor
this any
happens
the𝑛median
is defined
set of
numbers
to be the average of the 2 middle numbers.
𝑥51+, 𝑥82 , 𝑥13
3 … , 𝑥𝑛
=
= 6.5
There are 3 common2measures
of central tendency.
2
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
WhenFor
this any
happens
the𝑛median
is defined
set of
numbers
to be the average of the 2 middle numbers.
𝑥51+, 𝑥82 , 𝑥13
3 … , 𝑥𝑛
=
= 6.5
There are 3 common2measures
of central tendency.
2
MEDIAN: The middle number (in value) in the set of numbers.
But what if there is no single number in the middle?
Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9
Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9
This time there are 2 middle numbers.
The median is 6.5.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Before doing an example, let’s look at notation often used for the mean.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Before doing an example, let’s look at notation often used for the mean.
𝑥
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Before doing an example, let’s look at notation often used for the mean.
𝑥
This is the standard mathematical symbol for the mean.
It is pronounced ‘x bar’.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Before doing an example, let’s look at notation often used for the mean.
𝑥
This is the standard mathematical symbol for the mean.
It is pronounced ‘x bar’.
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥𝑖
𝑥=
=
𝑛
𝑛
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Before doing an example, let’s look at notation often used for the mean.
𝑥
This is the standard mathematical symbol for the mean.
It is pronounced ‘x bar’.
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥𝑖
𝑥=
=
𝑛
𝑛
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Technically,
statistics,
the sample mean.
Forinany
set of𝑥𝑛isnumbers
If we draw a random sample
𝑥1from
, 𝑥2 , a𝑥3population,
… , 𝑥𝑛 𝜇 denotes the mean of
theThere
wholeare
population
from measures
which the sample
was drawn
while 𝑥
3 common
of central
tendency.
denotes the mean of the sample drawn from the population.
MEAN:
The ordinary
average
of the statistics,
set of numbers.
Because
we are notarithmetic
focusing much
on inferential
the
difference
between
theselet’s
two look
things
terribly
important
usmean.
here.
Before
doing
an example,
at isn’t
notation
often
used fortothe
𝑥
This is the standard mathematical symbol for the mean.
It is pronounced ‘x bar’.
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥𝑖
𝑥=
=
𝑛
𝑛
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
numbers
𝑥1For
+any
𝑥2set
+ of⋯𝑛+
𝑥𝑛
𝑥𝑖
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛 =
𝑥=
𝑛
𝑛
There are 3 common measures
of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
(Round answer to 2 decimal places.)
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
numbers
𝑥1For
+any
𝑥2set
+ of⋯𝑛+
𝑥𝑛
𝑥𝑖
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛 =
𝑥=
𝑛
𝑛
There are 3 common measures
of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
(Round answer to 2 decimal places.)
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥=
𝑛
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
numbers
𝑥1For
+any
𝑥2set
+ of⋯𝑛+
𝑥𝑛
𝑥𝑖
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛 =
𝑥=
𝑛
𝑛
There are 3 common measures
of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
(Round answer to 2 decimal places.)
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥=
𝑛
3+3+8+3+1+5+8+8+8
𝑥=
9
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
numbers
𝑥1For
+any
𝑥2set
+ of⋯𝑛+
𝑥𝑛
𝑥𝑖
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛 =
𝑥=
𝑛
𝑛
There are 3 common measures
of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
(Round answer to 2 decimal places.)
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥=
𝑛
3 + 3 + 8 + 3 + 1 + 5 + 8 + 8 + 8 47
𝑥=
=
9
9
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
numbers
𝑥1For
+any
𝑥2set
+ of⋯𝑛+
𝑥𝑛
𝑥𝑖
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛 =
𝑥=
𝑛
𝑛
There are 3 common measures
of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8
(Round answer to 2 decimal places.)
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑥=
𝑛
3 + 3 + 8 + 3 + 1 + 5 + 8 + 8 + 8 47
𝑥=
=
= 5.22
9
9
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
This might be a good time to mention that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
MATH 110
14-2
Lecture:
Statistics-Measures
Central
Tendency
USING
THE Sec
CASIO
fx-260
TO FIND
THE MEAN OF AofSET
OF NUMBERS
1. Press
. (There are
but𝑛this
is one way to clear old data.)
Forother
anyways,
set of
numbers
2. Press
. (Puts calculator
tell if it is in stats
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
the Casio fx-260 calculator
5.
After
all data
in, press
. that
Be careful!
has a ‘stats mode’ that you can use to calculate means for you.
Some
people forget to press
6. You will find the mean in the calculator
display.
after the last number.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found on this summary sheet.
USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS
Forother
anyways,
set of
numbers
1. Press
. (There are
but𝑛this
is one way to clear old data.)
𝑥1 , 𝑥2in, 𝑥stats
, 𝑥𝑛
2. Press
. (Puts calculator
tell if it is in stats
3 …mode…can
by seeing
‘SD’ in the upper
right corner
of display.)
There are 3mode
common
measures
of central
tendency.
3. Key in the first number and press
.
MEAN:
arithmetic
average ofafter
the set
numbers.
4. Key inThe
eachordinary
succeeding
number, pressing
eachofone.
This
might
be a is
good
time to mention
5.
After
all data
in, press
. that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
6. You will find the mean in the calculator display.
Other useful tips
•Press
to display how many numbers you have entered.
• Once a number is entered, pressing
enters it again.
• These things and more can be found on this summary sheet.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
This might be a good time to mention that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
For any set of 𝑛 numbers
𝑥1 , 𝑥2 , 𝑥3 … , 𝑥𝑛
There are 3 common measures of central tendency.
MEAN: The ordinary arithmetic average of the set of numbers.
This might be a good time to mention that the Casio fx-260 calculator
has a ‘stats mode’ that you can use to calculate means for you.
You may be required to calculate a mean, median or mode from data
presented in a frequency table.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mode of the data in the
Score
Frequency
frequency table.
12
1
15
1
17
20
21
3
3
1
26
4
32
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mode of the data in the
Score
Frequency
frequency table.
12
1
Because a frequency table already has
15
1
counts, finding the mode is easy…
just find the score with the largest
17
3
frequency.
20
3
21
1
26
4
32
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mode of the data in the
Score
Frequency
frequency table.
12
1
Because a frequency table already has
15
1
counts, finding the mode is easy…
just find the score with the largest
17
3
frequency.
20
3
21
1
26
4
32
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mode of the data in the
Score
Frequency
frequency table.
12
1
Because a frequency table already has
15
1
counts, finding the mode is easy…
just find the score with the largest
17
3
frequency.
20
3
21
1
26
4
32
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mode of the data in the
Score
Frequency
frequency table.
12
1
Because a frequency table already has
15
1
counts, finding the mode is easy…
just find the score with the largest
17
3
frequency.
20
3
21
1
The mode is 26.
26
4
32
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
12
1
15
1
17
20
21
3
3
1
26
4
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
26
32
The mode is 26.
4
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
There is
Find the median of the data in the
Score one 12
Frequency
frequency table.
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
There is
Find the median of the data in the
Score one 12
Frequency
frequency table.
one
1
12
1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score ThereFrequency
is
frequency table.
1
12 one 15 1
We need for the data to be in order to
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score ThereFrequency
is
frequency table.
1
12 one 15 1
We need for the data to be in order to
two
2
15
1
find the median. Here the scores are
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
There
We need for the data to be in order to
2
15 are three 1
find the median. Here the scores are
17’s.
already in order BUT we have to be
17
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
There
We need for the data to be in order to
2
15 are three 1
find the median. Here the scores are
17’s.
already in order BUT we have to three
be
17
3
3
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
There
We need for the data to be in order to
2
15 are three 1
find the median. Here the scores are
17’s.
already in order BUT we have to be
four
17
3
4
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
There
We need for the data to be in order to
2
15 are three 1
find the median. Here the scores are
17’s.
already in order BUT we have to be
five
17
3
5
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
20
3
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
20
3
6
the frequencies into considerationsix
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
seven
20
3
7
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
eight
20
3
8
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
eight
20
3
8
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
Let’s count down to the 8th score in the table.
The 8th score in the table is 20.
32
The mode is 26.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the median of the data in the
Score
Frequency
frequency table.
1
12
1
We need for the data to be in order to
2
15
There 1
find the median. Here the scores are
already in order BUT we have to be
17 are three 3
5
20’s.
careful because we do have to take
eight
20
3
8
the frequencies into consideration
when finding the middle value.
21
1
There are 15 scores
26
4
That means that the 8th score is the median.
XXXXXXXXXXXXXXX
32
The mode is 26.
Let’s count down to the 8th score in the table.
The median is 20.
The 8th score in the table is 20.
2
MATH
Secas
14-2
Statistics-Measures
of Central Tendency
Note
that110
as long
theLecture:
total number
is not too
large,
wethe
could
just write
outdata
all the
first. Score
Find
median
of the
in numbers
the
Frequency
table.
12 15 17 17frequency
17 20 20 20
21 26 26 26 26 32 32
We need for the data to be in order to
find the median. Here the scores are
already in order BUT we have to be
careful because we do have to take
the frequencies into consideration
when finding the middle value.
There are 15 scores
12
15
1
1
17
20
21
3
3
1
26
4
32
The mode is 26.
The median is 20.
2
MATH
Secas
14-2
Statistics-Measures
of Central Tendency
Note
that110
as long
theLecture:
total number
is not too
large,
wethe
could
just write
outdata
all the
first. Score
Find
median
of the
in numbers
the
Frequency
table.
12 15 17 17frequency
17 20 20 20
21 26 26 26 26 32 32
We need for the data to be in order to
find the median. Here the scores are
already in order BUT we have to be
careful because we do have to take
the frequencies into consideration
when finding the middle value.
There are 15 scores
12
15
1
1
17
20
21
3
3
1
26
4
32
The mode is 26.
The median is 20.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
15
1
17
20
21
3
3
1
26
4
32
The mode is 26.
The median is 20.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
17
20
21
3
3
1
26
4
32
The mode is 26.
The median is 20.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
17
3
20
3
21
1
26
32
The mode is 26.
The median is 20.
4
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.old data.)
1. Press
. (There are other ways, but this isThe
onemedian
way to clear
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
The median is 20.
2. Press
. (Puts calculator in stats mode)
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
3. Key in the first number and press
. The median is 20.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES 17 goes in 3 times
12
15
17
17
3
20
3
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
1
20 goes in 3 times
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
21
1
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
26 goes in 4 times
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
32 goes in 2 times
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
is 20.one.
4. Key in each succeeding number, pressingThe median
after each
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
The median is 20.
5. After all data is in, press
.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
The median is 20.
6. You will find the mean in the calculator display.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
32
2
TheOF
mode
is 26.
USING THE CASIO fx-260 TO FIND THE MEAN
A SET
OF NUMBERS
The median is 20.
6. You will find the mean in the calculator display.
The mean is 21.8.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Find the mean of the data in the
Score
Frequency
frequency table.
12
1
We will use the calculator stats mode.
15
1
KEYSTROKES
12
15
17
17
3
20
3
20
21
26
21
1
32
26
4
The mean is 21.8.
32
The mode is 26.
The median is 20.
2
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
MEDIAN
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
MEDIAN
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
𝑄1
MEDIAN
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
The set of numbers above the median is called the upper half.
𝑄1
MEDIAN
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
The set of numbers above the median is called the upper half.
The median of the upper half is called the third quartile (called 𝑄3 ).
𝑄1
MEDIAN
𝑄3
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
The set of numbers above the median is called the upper half.
The median of the upper half is called the third quartile (called 𝑄3 ).
With the minimum value and maximum value, we have the 5 numbers.
MINIMUM
𝑄1
MEDIAN
𝑄3
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number Summary
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
The set of numbers above the median is called the upper half.
The median of the upper half is called the third quartile (called 𝑄3 ).
With the minimum value and maximum value, we have the 5 numbers.
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
The Five-Number Summary is a set of 5 numbers that, in some sense,
describes or summarizes a dataset.
DEFINITION: The Five-Number Summary
The median divides a dataset into two halves.
The set of numbers below the median is called the lower half.
The median of the lower half is called the first quartile (called 𝑄1 ).
The set of numbers above the median is called the upper half.
The median of the upper half is called the third quartile (called 𝑄3 ).
With the minimum value and maximum value, we have the 5 numbers.
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
X X X X X X X X X X X X X X X X
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MEDIAN
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MEDIAN
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
𝑄1
MEDIAN
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
𝑄1
MEDIAN
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
𝑄1
MEDIAN
𝑄3
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
60 + 61
= 60.5
2
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
The Five-Number
FIVE-NUMBER SUMMARY:
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚 ,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛 , 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Five-Number
FIVE-NUMBER
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚
,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛
, 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
We SUMMARY:
often The
represent
the Five-Number
Summary
By a graph called a Box-and-Whisker Plot.
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Five-Number
FIVE-NUMBER
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚
,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛
, 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
We SUMMARY:
often The
represent
the Five-Number
Summary
By a graph called a Box-and-Whisker Plot.
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
We
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
Draw a BOX from 𝑄1 to 𝑄3
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Five-Number
FIVE-NUMBER
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚
,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛
, 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
We SUMMARY:
often The
represent
the Five-Number
Summary
By a graph called a Box-and-Whisker Plot.
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
We
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
Extend WHISKERS from the box to min and max.
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency
Five-Number
FIVE-NUMBER
{𝑚𝑖𝑛𝑖𝑚𝑢𝑚
,Summary
𝑄1 , 𝑚𝑒𝑑𝑖𝑎𝑛
, 𝑄3 , 𝑚𝑎𝑥𝑖𝑚𝑢𝑚}
We SUMMARY:
often The
represent
the Five-Number
Summary
By a graph called a Box-and-Whisker Plot.
This is a list of ages of presidents assuming office between 1901 and 1993.
Construct the Five-Number Summary.
We
LOWER HALF
UPPER HALF
42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69
MINIMUM
𝑄1
MEDIAN
𝑄3
MAXIMUM
FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 }
This presentation can be found at:
http://cas.ua.edu/mtlc/UAMath110/LecNotes/Statistics/MATH110Sec14-2Lecture.pptx
Some extra practice exercises can be found at:
http://cas.ua.edu/mtlc/UAMath110/Exercises/Sec14-2Exercises.pdf
(with step-by-step solutions at:
http://cas.ua.edu/mtlc/UAMath110/Exercises/MATH110Sec14-2PracExercisesSOL.pptx)