vdoc

Chapter 18: A. Basic Statistics and Applications 201
The mean is also sometimes referred to as the arithmetic mean, and is the most
useful and most commonly used measure of centrality. The median is the second
most used, and mode is the least used measure of centrality.
Mean. The mean of a sample or population data is calculated by taking the sum
of the data measurements and then dividing the sum by the number of measurements
in the sample or the population data. The mean of a sample is called the sample
mean and is denoted by X – (read as X-bar) and the population mean is denoted by
the Greek letter m (read as mu). These terms are defined numerically as follows:
X + X + … + X X
1 2 N i
Population mean m =
=
N
N
(18.1)
Sample mean X X + X + … + X X
1 2 n i
=
=
n
n
(18.2)
Where (read as sigma) is symbolized as a summation over all the measurements,
and where N and n denote the population and sample size respectively.
EXAMPLE 18.1
The data in this example give the hourly wages (in dollars) of some randomly selected
workers in a manufacturing company.
8, 6, 9, 10, 8, 7, 11, 9, 8
Find the mean hourly wage of these workers.
Solution:
Since wages listed in these data are only for some of the workers in the company, it represents
a sample. Thus, we have:
So the sample mean is
n = 9
x i = 8 + 6 + 9 + 10 + 8 + 7 + 11 + 9 + 8 = 76.
x
X = 1
76
= =
n 9
844 .
Part IV.A.1
In this example, the mean hourly wage of these employees is eight dollars and fortyfour
cents an hour.