Essential Statistics

Chapter 2: Measures of Central Tendency

The most commonly used measures of central tendency for sample data are

the mean, the median, and the mode. These measures will be discussed in

this chapter along with their properties.

The first measure of central tendency which will be discussed is the mean.

2-2 The Mean

Generally speaking, the mean of a set of numerical values is the arithmetic

average of the set of values. Thus the mean for a set of numerical values is

obtained by adding the values and dividing this sum by the number of values

which are in the data set.

Keep in mind that we can analyze data from either a sample or a population

or from both. Because of this, we may have to compute the mean for sample

data or the mean for population data.

Notes:



When computing the value of the mean, the data values can be

population values or sample values.



Hence we can compute either the population mean or the sample

mean.

First we will introduce the idea of the sample mean.

Definition: Sample Mean

The mean of a sample set of numerical data values is the arithmetic average

for the set of values.

In statistics, we usually use notations or symbols to represent some of the

concepts which are studied. We will start with the symbolic notation for the

sample mean.

Notation:

The sample mean is usually denoted by the symbol

. This

notation is read as “

-bar”.