Basic Mathematics for College Students

If there is an even number of values in a set, there is no middle value. In that case,

the median is the mean (average) of the two values closest to the middle.

614 Chapter 7 Graphs and Statistics

EXAMPLE (^5) Find the median of the following set of values:
7.5 20.9 9.9 4.4 9.8 5.3 6.2 7.5 4.9
StrategyWe will arrange the nine values in increasing order.
WHYIt is easier to find the middle value when they are written in that way.
Solution
Since there is an odd number of values, the median is the middle value.
Smallest 4.4 4.9 5.3 6.2 7.5 9.8 9.9 20.9 Largest
Four values Four values
The middle value
The median is 7.5

⎧⎪⎪⎪⎨⎪⎪⎪⎩ 7.5 ⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

Self Check 5

Find the median of the following

set of values:

Now TryProblems 17 and 21

1

7

8

2

1

2

3

3

5

1

2

2

3

4

EXAMPLE (^6) Grade Distributions On an exam, there were three
scores of 59, four scores of 77, and scores of 43, 47, 53, 60, 68, 82, and 97. Find the
median score.
StrategyWe will arrange the fourteen exam scores in increasing order.
WHYIt is easier to find the two middle scores when they are written in that way.
Solution
Since there is an even number of exam scores, we need to identify the two middle
scores.
Smallest Largest
Six scores Six scores
Two middle scores
Since there is an even number of scores, the median is the average (mean) of the
two scores closest to the middle: the 60 and the 68.
The median is 64.
Median

60  68

2



128

2

 64

⎧⎪⎪⎪⎪ ⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩  ⎧⎪⎪⎪⎪ ⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

43 47 53 59 59 59 60 68 77 77 77 77 82 97

Self Check 6

GRADE DISTRIBUTIONSOn a

mathematics exam, there were

four scores of 68, five scores of

83, and scores of 72, 78, and 90.

Find the median score.

Now TryProblems 25 and 29

Success Tip The median 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 Example 5, the

median, 7.5, was one of the given values. In Example 6, the median exam

score, 64, was not in the given set of exam scores.

Find the mode of a set of values.

The mean and the median are not always the best measure of central tendency. For

example, suppose a hardware store displays 20 outdoor thermometers. Ten of them

read 80, and the other ten all have different readings.

To choose an accurate thermometer, should we choose one with a reading that is

closest to the meanof all 20, or to their median?Neither. Instead, we should choose

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