Transcript Remember the 3 Ms? Mean, Median, and Mode Section 3.3

Remember the 3 Ms?
Mean, Median, and Mode
~Central Tendency~
Objective
The student will be able to calculate
measures of central tendency
(mean, median, and mode)
Mean = Average
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2.
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The mean is the average of a data set
To find the mean:
Find the sum of the data items
Divide by the number of data items.
The mean will Always be greater than the smallest number
and less than the largest number.
These are data items:
2, 3, 4, 5, 8, 8, and 12
2 + 3 + 4 + 5 + 8 + 8 + 12
7 (total data items)
42 / 7 = the mean, which is 6
Mean is the average of a
set of data. To calculate
the mean, find the sum
of the data and then
divide by the number of
data.
Central Tendency
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The Central Tendency is the center of the
distribution of a data set.
The mean of a set of data is the most
common measure of Central Tendency.
Other measures are mode and median
A way to remember…Mean – It is very
mean because it makes you do all that
work! grrrrrrrrr
You try the next one!
ABC Warehouse sells
flat screen TVs at the
following prices: $350,
$275, $500, $325,
$100, $375, and $300.
What is the mean
price?
Outliers
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Values that are much
higher or lower than
others in a data set are
Outliers.
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High temperatures
Monday through Friday
were 80, 81, 60, 77, and
82. Identify the outlier
in the data.
Median
What does this word make you think of…
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The middle number of a set of data, arranged in
numerical order
Median is the middle of the road
How Tall are You?
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Need 5 volunteers:
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Need 1 more volunteer
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What is the median height?
What is the median height?
What was different about our middle number?
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Odd Number of Data Items:
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the middle number when the data items are put in numerical
order.
Even Number of Data Items:
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the two middle numbers when data items are put in numerical
order.
Median
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Find the median of this data set
4, 3, 7, 9, 5, 3, 1
Put them in order!
There are 7 numbers in total…looking for
the “middle” number
Median =
Mode
What does this word make you think of?
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Mode: the data item that occurs the MOST
What is the mode from our previous data set?
4, 3, 7, 9, 5, 3, 1
3 is a mode for these data items.
How old are you?
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Raise your hand if you are:
13
14
15
16
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What is the mode?
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Mean
The average
Median
The number or
average of the
numbers in the
middle
Mode
The number that
occurs most
Find me the M, M & Ms
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12, 14, 26, 37, 8, and 14
Re-order: 8, 12, 14, 14, 26, 37, 26.
Mean: 19.6
Median: 14
How many Modes: 2
Mode: 14, 26
Find me ONLY Mode:
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Grape, grape, banana, nectarine, strawberry,
strawberry, strawberry, orange, watermelon.
How many modes?
Just one: strawberry.
Find me the M, M & Ms
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2.3, 4.3, 3.2, 2.9, 2.7, and 2.3.
Re-order: 2.3, 2.3, 2.7, 2.9, 3.2, 4.3.
Mean: 2.95
Median: 2.8
How many Modes? 1
Mode: 2.3
Outlier
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Outlier: is a data item (data value) that is
much higher or lower than the other data
values.
Outliers can affect the mean of a group of
data.
Example: 2, 3.5, 1, 2,
5,000,000.
Example: 35, 45, 40, 37, -6.
Describing Data with M, M, & M.
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You can use what you know about Mean,
Median, and Mode to describe data.
But figuring out which M describes it best is
difficult.
Nah! Its got to
be mean!
I think mode
describes it best!
Which M, M, & M is best?
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The favorite movie of students in the eighth
grade class?
Mode: good for non-numerical data items and
for frequent occurrences.
Which M, M, & M is best?
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The distances students in your class travel to
school.
Median: one student may live much further
than everyone else. When an outlier may
significantly influence the mean, we use
median.
Which M, M, & M is best?
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The daily high temperature during a week in
July.
Mean: since daily temp. are not likely to have
outlier, mean is best. When data have no
outlier, use mean.
Measures and Central Tendency
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Your text book is going to ask you determine
which MEASURE of CENTRAL TENDENCY best
describe the data.
Its just asking you to figure out which M
works with the data best!