Study Guide and Intervention (continued) - MathnMind

13-4
Quartiles and Interquartile Range Three quartiles divide data into four equal
parts. The upper quartile divides the top half into two equal parts. The lower quartile
divides the bottom half into two equal parts. The middle quartile is the median of the
data. The upper and lower quartile values are used to determine the interquartile range,
another measure of variation
Example
Find the lower quartile, the upper quartile, and the interquartile
range for the data set 23, 23, 31, 31, 63, 63, 69, 71, 72, 82, 88, 160.
Step 1 Find the median.
The data are already in order. Since there are an even number of values, the median
is the average of the middle two values, 63 and 69. The median is 66.
Step 2 Find the median of the lower half.
There are two middle values of the lower half of the data, both of which are 31.
So 31 is the lower quartile.
Step 3 Find the median of the upper half.
The middle value of the upper half of the data is the average of the middle two
values, 72 and 82. This average is 77. So 77 is the upper quartile.
Step 4 The interquartile range is 77 31 or 46.
Exercises
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Measures of Variation
Find the median, lower quartile, upper quartile, and interquartile range of each
set of data.
1. 2.
Tallest Trees of the U.S.
Type of Tree Height in Feet
Giant Sequoia 275
Giant Redwood 321
Sitka Spruce 191
Coast Douglas Fir 281
Sugar Pine 232
Port Orford Cedar 219
Source: The World Almanac
3. 4, 5, 5, 4, 4, 6, 5, 7, 9, 9 4. 1, 7, 12, 10, 21, 32, 24, 19
5. 3, 0, 4, 8, 5, 4, 0, 1, 7, 9, 2, 4, 8 6. 80, 90, 94, 95, 100, 102, 83, 94, 78
7. 8. Stem | Leaf
Stem | Leaf
1 | 0356788
2 | 1456778
3 | 00123
4 | 689 1⏐0 10
20 | 346799
21 | 0068
22 | 122578
23 | 3478 20⏐3 203
© Glencoe/McGraw-Hill 800 Glencoe Algebra 1
0
10
20
30
40
50
60
70
80
90