Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 12-2

Example 1	Range
Find the range of each set of data.
a.	{3, 9, 1, 11, 15, 7, 8}

The greatest value is 15 and the least value is 1. So, the range is 15 – 1 or 14.

Stem | Leaf

2
3
4

6 7 7 9
0 1 4 5 5 8
2 6 9

| 42 = 42

b.	

The greatest value is 49 and the least value is 26. So, the range is 49 – 26 or 23.

Example 2	Interquartile Range and Outliers
Find the interquartile range and any outliers for {6, 11, 3, 18, 7, 5, 13, 9}.

Step 1	List the data from least to greatest.  Then find the median.

3     5     6     7     9     11     13     18
	
median =  or 8

Step 2	Find the upper and lower quartiles.

upper half

lower half

median = 8

	3  5  6  7  9  11  13  18

UQ =   or 12

LQ =   or 5.5

The interquartile range is 12 – 5.5 or 6.5.

Step 3	Find the limits for the outliers.
		Multiply the interquartile range, 6.5 by 1.5.		6.5 × 1.5 = 9.75
		Subtract 9.75 from the lower quartile.		5.5 -9.75 = -4.25
		Add 9.75 to the upper quartile.			12 + 9.75 = 21.75

The limits for the outliers are -4.25 and 21.75.  There are no values less than -4.25 or greater than 21.75.  So, the are no outliers in the data set.

Example 3	Interpret and Compare Data
MARRIAGE	The ages at which men and women first get married are listed in the stem-and-leaf plot.

Men | | Women

9
8 6 3 3 2
9 7 6 5 5 4 0
6 2
1
4

1
2
3
4
5
6

8 8 9
0 1 1 3 5 9
2 4 7
1
3 6

03 = 30 years | | 23 = 23 years

a.	What is the median age for each group?
The median age for the men is 35.
The median age for the women is 25.

b.   Compare the range for the men and the women.
The range for the men is 64 – 19 or 45 years and the range for the women is 56 – 18 or 38 years. So, the ages vary more for the men than the women.