Transcript Power Point for Measures of Central Tendency

Measures of Central
Tendency
What Are Measures of
Central Tendency?
What Are Measures of
Central Tendency?
By Measures of Central Tendency,
we are referring to a variety of
measurements of a set of data.
What Are Measures of
Central Tendency?
Each of these measurements will
result in a single number that
represents the data set in a
specific way.
There are 3 Measures of
Central Tendency
These are:
These are:
Mean
•
These are:
Mean
•Median
•
These are:
Mean
•Median
•Mode
•
Let’s begin with an
explanation of Mean
Mean
The Mean of a set of data
is the average value of all
of the numbers in the set.
Mean
For example, let’s consider this set
of numbers:
{4, 7, 9, 11, 14}
Mean
{4, 7, 9, 11, 14}
First, add up all of the numbers in
the set.
4 + 7 + 9 + 11 + 14 = 45
Mean
{4, 7, 9, 11, 14}
Next, count the “number of
numbers” in the set.
There are 5 numbers in this set.
Mean
{4, 7, 9, 11, 14}
Finally, divide the sum of all the numbers in the
set by the “number of numbers” in the set.
4 + 7 + 9 + 11 + 14 = 45
There are 5 numbers in this set.
45 ÷ 5 = 9
Mean
{4, 7, 9, 11, 14}
45 ÷ 5 = 9
The mean of this set is equal to 9
Mean
Now, try one on your own:
Determine the mean of this set of data:
{12, 15, 22, 25, 36, 40}
Mean
{12, 15, 22, 25, 36, 40}
The mean of this set of data is:
22
24
25
35
Mean
CORRECT!
{12, 15, 22, 25, 36, 40}
The mean of this set of data is:
25
Mean
Sorry, but that’s not quite right. Perhaps
a little review would help.
Next Step
Now that you have a good understanding
of mean, let’s go on to the next Measure
of Central Tendency which is the
Median
Median
Think about driving down the interstate.
Most of the time, there is an area of
grass between the two strips of highway.
This grassy area is called the median
because it is in the middle of the
interstate
Median
In a similar way, the median of a set of
numbers is the number that is exactly in
the middle of the set.
Median Example
Consider again this set of data:
{4, 7, 9, 11, 14}
Median Example
{4, 7, 9, 11, 14}
The number 9 has two numbers to its left
and two numbers to its right, so it is in
the middle of this set of data.
Median Example
{4, 7, 9, 11, 14}
Since the number 9 is in the middle of this set
of data, 9 is the median.
On Your Own
Try a problem where you determine the
median of a set of data on your own now.
Try This One
Determine the median of this set of data:
{3, 6, 12, 19, 23, 29, 32}
Try This One
{3, 6, 12, 19, 23, 29, 32}
The median of this set of data is:
6
12
19
23
Good Job!
Correct!
The median of this set of data is 19
Now let’s continue …
Ascending Order
{3, 6, 12, 19, 23, 29, 32}
One thing that you may notice about the
set of data you just worked with is that it
is already arranged in ascending order.
Ascending Order
{3, 6, 12, 19, 23, 29, 32}
This means that the numbers start from
the smallest. The next one is the next
largest, and they continue on this way to
the largest one.
Ascending Order
When calculating mean or mode, the
order of the data doesn’t matter.
However, when calculating median, the
numbers must be in ascending order.
Example of Ascending Order
You’ll notice that the set of data below is
not in ascending order.
{14, 2, 47, 32, 12, 53, 29}
Example of Ascending Order
To find median, we must place these numbers in
ascending order:
{14, 2, 47, 32, 12, 53, 29}
equals:
{2, 12, 14, 29, 32, 47, 53}
Example of Ascending Order
The middle number of this set, or the
median, is the number 29.
{2, 12, 14, 29, 32, 47, 53}
Practice
Now try another one on your own.
Practice
Determine the median of the following
set of data:
{41, 13, 63, 28, 4, 55, 30}
Practice
{41, 13, 63, 28, 4, 55, 30}
The median of this set of data is:
28
30
41
55
Good Job!
Correct!
The median of this set of data is 30
An Even Number of Numbers
So far, all of the data sets we have
looked at to determine median have
contained an odd number of terms, or
numbers.
It is very easy to find the middle number
in a set if the number of terms is odd.
An Even Number of Numbers
Sometimes though, the number of terms
in a set is even.
This requires some additional thought to
determine the median of such a set.
An Even Number of Numbers
For example, consider this set of data:
{2, 5, 8, 12, 13, 16}
An Even Number of Numbers
{2, 5, 8, 12, 13, 16}
First of all, these numbers are in
ascending order, so we don’t have to
worry about that.
However, there is no number directly in
the middle of the data set!
Finding the Middle Number
{2, 5, 8, 12, 13, 16}
When there is an even number of terms
in a data set, we must find the middle
two numbers.
In this case, the two numbers in the
middle are 8 and 12.
Finding the Middle Number
{2, 5, 8, 12, 13, 16}
To determine the median of this set of
data, we now take the two middle
numbers and find the mean of those.
Finding the Middle Number
{2, 5, 8, 12, 13, 16}
The two middle numbers are 8 and 12.
Find the mean of 8 and 12:
8 + 12 = 20
20 ÷ 2 = 10
Finding the Middle Number
{2, 5, 8, 12, 13, 16}
8 + 12 = 20
20 ÷ 2 = 10
The median of this set of data is 10.
Practice
Now, try one on your own.
Practice
Determine the median of this set of data:
{5, 8, 13, 20, 24, 34, 42, 57}
Practice
{5, 8, 13, 20, 24, 34, 42, 57}
The median of this set of data is:
20
22
24
28
Good Job!
Correct!
The median of this set of data is 22
{5, 8, 13, 20, 24, 34, 42, 57}
Moving On …
Now that you have a good grasp of
the concepts of mean and median,
let’s learn about the mode of a set.
Mode
The mode of a set is the number
that appears most often in a set of
data.
Mode
The word mode begins with the
letters m and o …
The word most also begins with the
letters m and o
Mode = Most
Example of Mode
{16, 9, 2, 9, 8, 11, 9, 13, 11}
In the data set above, you will notice that the number 9
appears more often than any other number.
9 appears most often.
9 is the mode of this set.
(You may also notice that the order of terms did not matter)
Practice Finding the Mode
Now, try one on your own.
Practice Finding the Mode
Determine the mode of the following set
of data:
{31, 64, 89, 64, 31, 102, 31, 29}
Practice Finding the Mode
{31, 64, 89, 64, 56, 31, 102, 31, 29,}
The mode of the set of data is
31
56
64
102
Good Job!
Correct!
{31, 64, 89, 64, 56, 31, 102, 31, 29,}
The mode of this set of data is 31
Congratulations!
You have mastered the 3 Measures of
Central Tendency:
Mean, Median, and Mode.
Not Quite!
Sorry, but that’s not quite right.
Perhaps a little review will help.
Not Quite!
Sorry, but that’s not quite right.
Perhaps a little review will help.
Not Quite!
Sorry, but that’s not quite right.
Perhaps a little review will help.
Not Quite!
Sorry, but that’s not quite right.
Perhaps a little review will help.
End Of Tutorial
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