Basic Mathematics for College Students

7.2 Mean, Median, and Mode 609

SECTION 7.2

Mean, Median, and Mode

Objectives

1 Find the mean (average) of a set

of values.

2 Find the weighted mean of a

set of values.

3 Find the median of a set of

values.

4 Find the mode of a set of

values.

5 Use the mean, median, and

mode to describe a set of

values.

Graphs are not the only way of describing sets of numbers in a compact form. Another
way to describe a set of numbers is to find onevalue around which the numbers in the
set are grouped. We call such a value a measure of central tendency.In Section 1.9, we
studied the most popular measure of central tendency, the meanor average. In this
section we will examine two other measures of central tendency, called the medianand
the mode.

Find the mean (average) of a set of values.

Recall that the meanor averageof a set of values gives an indication of the “center”
of the set of values. To review this concept, let’s consider the case of a student who has
taken five tests this semester in a history class scoring 87, 73, 89, 92, and 84. To find out
how well she is doing, she calculates the mean, or the average, of these scores, by
finding their sum and then dividing it by 5.

In the numerator, do the addition.

Do the division.

The mean is 85. Some scores were better and some were worse, but 85 is a good
indication of her performance in the class.

Success Tip The mean (average) is a single value that is “typical” of a set of

values. It can be, but is not necessarily, one of the values in the set. In the

previous example, note that the student’s mean score was 85; however, she did

not score 85 on any of the tests.

Finding the Mean (Arithmetic Average)

The mean,or the average,of a set of values is given by the formula:

The Language of Mathematics The mean(average) of a set of values is

more formally called the arithmetic mean(pronounced air-rith-MET-tick).

Mean ( average )

the sum of the values

the number of values

 85



425

5

85

5  425

 40

25

 25

0

8

2

7

73

89

92

 84

425

The sum of the test scores

 The number of test scores



Mean

87  73  89  92  84

5

1

EXAMPLE (^1) Store Sales One week’s sales in men’s, women’s, and
children’s departments of the Clothes Shoppe are given in the table on the next
page. Find the mean of the daily sales in the women’s department for the week.
StrategyWe will add $3,135, $2,310, $3,206, $2,115, $1,570, and $2,100 and divide
the sum by 6.
Self Check 1
STORE SALESFind the mean of
the daily sales in the men’s
department of the Clothes
Shoppe for the week.
Now TryProblems 9 and 41