FINDING THE MEAN

One measure of center is the mean. The mean, or average, of a data set is the sum of the data values divided by the number of data values in the set.

Example

Peterson surveyed five of her friends to find out how many brothers and sisters they have. Her results are shown in the table.

Step 1 :

Model each person’s response as a group of counters.

Step 2 :

Now rearrange the counters so that each group has the same number of counters.

Step 3 :

Each group now has 2 counters. This value is the mean. This model demonstrates how the mean “evens out” the data values.

Step 4 : 

Use numbers to calculate the mean. 

The sum of the data values is

=  2 + 3 + 1 + 1 + 3

=  10

How many data values are in the set ?

5

Step 5 : 

Mean  =  Sum of data values / Number of data values

Mean  =  10 / 5

Mean  =  2

Reflect

1. Can the mean be greater than the greatest value in a data set ? Why or why not ?

No; the group(s) with the greatest number of counters will lose counters to other groups in order to “even out” the data set. So the mean will not be greater than the greatest value.

2. Suppose you have a data set in which all of the values are 2. What is the mean ?

2

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