GPS Unit 10Grade 7

Measures of Central

Tendency

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.

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.

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.

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.

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?

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.

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.

Example Find the mean, median, and mode score for the data in the table

below.

Score Frequency

10 22

9 36

8 40

7 17

Find the mean by following these

steps:

1. Determine the total number of students.

2. Use multiplication and addition together to find the total of all students’ scores.

3. Divide the sum of the scores by the total number of students.

Example Find the mean, median, and mode score for the data in the table

below.

Score Frequency

10 22

9 36

8 40

7 17

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.

Example Find the mean, median, and mode score for the data in the table

below.

Score Frequency

10 22

9 36

8 40

7 17

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.