Page 556 - Basic College Mathematics with Early Integers

SE CT I O N 7. 3 I MEAN, MEDIAN, AND MODE 533

Example 4 Find the median of the following list of scores: 67, 91, 75, 86, 55, 91 PRACTICE 4
Find the median of the list of
Solution: First we list the scores in numerical order and then find the middle scores:
number. 36, 91, 78, 65, 95, 95, 88, 71
55, 67, 75, 86, 91, 91
Since there is an even number of scores, there are two middle numbers, 75 and 86.
The median is the mean of the two middle numbers.
75 + 86
median = = 80.5
2
Don’t forget to write the
The median is 80.5.
numbers in order from smallest to
Work Practice 4 largest before finding the median.

Objective Finding the Mode

The last common measure of central tendency is called the mode.

The mode of a set of numbers is the number that occurs most often. (It is possible
for a set of numbers to have more than one mode or to have no mode.)

Example 5 Find the mode of the list of numbers:

11, 14, 14, 16, 31, 56, 65, 77, 77, 78, 79 PRACTICE 5

Solution: There are two numbers that occur the most often. They are 14 and 77. Find the mode of the list of
This list of numbers has two modes, 14 and 77. numbers:
14, 10, 10, 13, 15, 15, 15, 17, 18
Work Practice 5 18, 20

Example 6 Find the median and the mode of the following set of numbers. PRACTICE 6
These numbers were high temperatures for 14 consecutive days Find the median and the mode
in a city in Montana. of the list of numbers:

76, 80, 85, 86, 89, 87, 82, 77, 76, 79, 82, 89, 89, 92 26, 31, 15, 15, 26, 30, 16, 18,
15, 35
Solution: First we write the numbers in numerical order.
76, 76, 77, 79, 80, 82, 82, 85, 86, 87, 89, 89, 89, 92
Since there is an even number of items, the median is the mean of the two middle
numbers, 82 and 85.
82 + 85
median = = 83.5
2
The mode is 89, since 89 occurs most often.
Work Practice 6

Concept Check True or false? Every set of numbers must have a mean,
median, and mode. Explain your answer.

Don’t forget that it is possible for a list of numbers to have no mode. For exam-
Answers
ple, the list
4. 83 5. 15 6. median: 22; mode: 15
2, 4, 5, 6, 8, 9
Concept Check Answer
has no mode.There is no number or numbers that occur more often than the others. false; a set of numbers may have no
mode