Information Technology Reference
In-Depth Information
2.3 THE MEAN AS A MEASURE OF CENTRAL TENDENCY
2.3.1 GENERAL CONCEPTION OF THE MEAN
The arithmetic mean, or simply the
mean
, is the most common measure of
central tendency used in quantitative research. It is computed by summing
all of the scores in a distribution and dividing by the number of scores in
the distribution. The mean is generically referred to as an average and is a
part of our daily language. Students have encountered means when they
receive their grade point average from the Registrar's Office, sports fans
read with great anticipation baseball batting averages in newspaper sports
sections, and TV weather reporters update their local viewers on average
rainfall in inches.
2.3.2 NOTATION FOR THE MEAN
The mean is computed by adding the scores in a group and dividing this
value by the number of scores. A verbal account of an arithmetic procedure
can often be described more succinctly with a computational formula,
and throughout this text we will be providing computational formulas
and numerical examples for many of the key statistical processes we have
covered at a more conceptual level. For many readers, working out these
statistical analyses “by hand” with a calculator is an excellent way of rein-
forcing the conceptual lesson already conveyed and may provide a useful
comparative bridge to the SPSS and SAS statistical software output.
Before providing you with the computational formula for the mean,
we need to introduce some of the basic notational system that we will be
using throughout this text. The symbols we use in the formula for the
mean are shown in Table 2.1. Generally, the letter
Y
is used to denote
scores on the dependent variable. The subscript
i
in
Y
i
is used to repres
en
t
any score and thus is applicable to every score. A
Y
with a bar over it (
Y
)
represents the mean of the scores. Group size is symbolized as a lowercase
n
; full sample size is symbolized as an uppercase
N
.
2.3.3 FORMULA FOR THE MEAN
Nowwearereadytowriteourformulaforthemeanas
=
Y
n
Y
.
(2.1)
To see this formula in practice, consider the following numerical exam-
ple in Table 2.2. Suppose we sample a small group of newlyweds (
n
7)
and ask them as couples the following question: “How happy are you
at this time with your marriage?” They are asked to use the following
four-point scale:
=
very happy
=
1
happy
=
2
unhappy
3
very unhappy
=
=
4.
