1. Measures of Central Tendency
GPS Unit 10
Grade 7

2. What is a measure of central tendency?
Measures of central tendency summarize a set of data by giving some sense of the typical (or average) value.
The three most common measures of central tendency are the mean, median, and mode.

3. When would we use these?
Suppose we have test scores from two mathematics classes. What if we want to compare the two classes on the math test?
We need a way to compare the classes as a whole rather than considering individual scores. Measures of central tendency could help in this situation.

4. When should I use. . .
Mean? For sets of data with no unusually high or low numbers.
Median? For sets of data with some points that are much higher or lower than most of the others.
Mode? For sets of data points that are the same.

5. A mean is an average found by using addition and division.
What is the mean?
A mean is an average found by using addition and division.
The items in a data set are added together, and then the sum is divided by the number of items.

6. Uh oh! What if I have two middle numbers?
What is a median?
A median is an average found by identifying the number in the middle of the data set.
If the data set contains an even number of items and has two middle numbers, you must find the mean of the two middle numbers.
Uh oh! What if I have two middle numbers?

7. Here’s a clue for you!
Before you try to find a median or mode, make sure that the data values are ordered from least to greatest.

8. In the following set of data, the number 6 is the mode:
How do you find the mode?
In the following set of data, the number 6 is the mode:
0, 1, 2, 2, 5, 5, 6, 6, 6, 7, 7, 8
Here’s a clue. . .
The word mode starts with the same letters as most. Therefore, the mode is the number that occurs the most in a set of data.

9. Example
Find the mean, median, and mode score for the data in the table below.
Find the mean by following these steps:
Determine the total number of students.
Use multiplication and addition together to find the total of all students’ scores.
Divide the sum of the scores by the total number of students.
Score
Frequency 10 22 9 36 8 40 7 17

10. Example
Find the mean, median, and mode score for the data in the table below.
Finding the median:
Since there are 115 scores, the median is the 58th score.
To find the 58th score, examine the frequency column: there are 22 scores of 10, and then 36 scores of 9. Together, that makes 58 scores.
So, the 58th score is 9; therefore, it is the median.
Score
Frequency 10 22 9 36 8 40 7 17

11. Example
Find the mean, median, and mode score for the data in the table below.
Finding the mode:
Frequency represents the number of students that received a particular score.
Therefore, the score with the highest frequency will be the mode.
The mode is 8.
Score
Frequency 10 22 9 36 8 40 7 17