CK-12-Basic Probability and Statistics Concepts - A Full Course

5.1. Mean http://www.ck12.org

μ=∑

x 1 +x 2 +x 3 +...+xn

N

You can now use the formula to calculate the mean number of blocks per student:

μ=∑

x 1 +x 2 +x 3 +...+xn

N

μ=

2 + 6 + 12 + 25 + 18 + 28 + 24 + 18 + 30 + 33 + 12

30

μ=

208

30

μ≈ 6. 93

This means that, on average, each student picked 7 blocks from the pail.

Example A

Stephen has been working at Wendy’s for 15 months. The following numbers are the number of hours that Stephen
worked at Wendy’s for each of the past 7 months:

24 , 24 , 31 , 50 , 53 , 66 , 78

What is the mean number of hours that Stephen worked each month?

Step 1:Add the numbers to determine the total number of hours he worked.

24 + 25 + 33 + 50 + 53 + 66 + 78 = 329

Step 2:Divide the total by the number of months.
329
7 =^47

The mean number of hours that Stephen worked each month was 47.

Stephen has worked at Wendy’s for 15 months, but the numbers given above are for 7 months. Therefore, this set of
data represents a sample, which is a portion of the population. The formula that was used to calculate the mean of
the blocks must be changed slightly to represent a sample. The mean of a sample is denoted by ̄x, which is called “x
bar.”

The number of data values for a sample is written asn. The following formula represents the steps that are involved
in calculating the mean of a sample:

Mean=

sum of the values

the number of values

This formula can now be written using symbols:

x=∑

x 1 +x 2 +x 3 +...+xn

n