http://www.ck12.org Chapter 5. Measures of Central Tendency
You can now use the formula to calculate the mean number of hours that Stephen worked each month:
x=
∑x 1 +x 2 +x 3 +...+xn
n
x=24 + 25 + 33 + 50 + 53 + 66 + 78
7
x=329
7
x= 47The mean number of hours that Stephen worked each month was 47.
The formulas only differ in the symbol used for the mean and the case of the variable used for the number of data
values (Norn). The calculations are done the same way for both a population and a sample. However, the mean of
a population is constant, while the mean of a sample changes from sample to sample.
Example B
Mark operates a shuttle service that employs 8 people. Find the mean age of these workers if the ages of the 8
employees are as follows:
55 63 34 59 29 46 51 41
If you were to take a sample of 3 employees from the group of 8 and calculate the mean age for these 3 workers,
would the result change?
Since the data set includes the ages of all 8 employees, it represents a population. The mean age of the employees
can be calculated as shown below:
μ=∑
x 1 +x 2 +x 3 +...+xn
N
μ=55 + 63 + 34 + 59 + 29 + 46 + 51 + 41
8
μ=378
8
μ= 47. 25The mean age of all 8 employees is 47.25 years, or 47 years and 3 months.
Now let’s take 2 samples of 3 employees from the group of 8 and calculate the mean age for these samples to see
if the result changes. Let’s use the ages 55, 29, and 46 for one sample of 3, and the ages 34, 41, and 59 for another
sample of 3:
x=
∑x 1 +x 2 +x 3 +...+xn
n
x=
∑x 1 +x 2 +x 3 +...+xn
n
x=55 + 29 + 46
3
x=34 + 41 + 59
3
x=130
3
x=134
3
x= 43. 33 x= 44. 66