1. Lesson 13-4
Measures of Variation

2. Click the mouse button or press the Space Bar to display the answers.
Transparency 4

3. Transparency 4a

4. Objectives Find the range of a set of data
Find the quartiles and the Interquartile range of a set of data

5. Vocabulary range – measures of variation – quartiles –
lower quartile –
upper quartile –
Interquartile range –
outlier –

6. Measure of Dispersion How spread out is the data?
Range is one measure (biggest – smallest value)
A quartile (Q) is one-quarter of the ordered data set (25%)
The median is the second quartile (Q2)
The interquartile range or IQR (Q3 – Q1) is a measure of the spread of the middle of the data set
The IQR is used in statistics to identify outliers in the data
Range Q1 Q2 Q3
25%
25%
25%
25%
smallest
biggest
Interquartile Range

7. Example 1
College Football The teams with the top 15 offensive yardage gains for the 2000 season are listed in the table. Find the range of the data.
Team
Yardage
Air Force
Boise St.
Clemson
Florida St.
Georgia Tech
Idaho
Indiana
Kentucky
Miami
Michigan
Nebraska
Northwestern
Purdue
Texas
Tulane
4971
5459
4911
6588
4789
4985
4830
4900
5069
5059
5232
5183
4825
4989
The greatest amount of yardage gains is 6588, and the least amount of yardage gains is 4789.
Answer: The range of the yardage is or 1799 yards.

8. Area (thousand square miles)
Example 2
Geography The areas of the 5 largest states are listed in the table. Find the median, the lower quartile, the upper quartile, and the interquartile range of the areas.
State
Area (thousand square miles)
Alaska
California
Montana
New Mexico
Texas
656
164
147
124
269
Explore You are given a table with the areas of the 5 largest states. You are asked to find the median, the lower quartile, the upper quartile, and the interquartile range.

9. Example 2 cont
Plan First, list the areas from least to greatest. Then find the median of the data. The median will divide the data into two sets of data. To find the upper and lower quartiles, find the median of each of these sets of data. Finally, subtract the lower quartile from the upper quartile to find the interquartile range.
Solve
median

10. Example 2 cont Answer: The median is 164 thousand square miles.
The lower quartile is thousand square miles and the upper quartile is thousand square miles.
The interquartile range is – or 327 thousand square miles.
Examine Check to make sure that the numbers are listed in order. Since 135.5, 164, and divide the data into four equal parts, the lower quartile, median, and upper quartile are correct.

11. Example 3 Identify any outliers in the following set of data. Stem
Leaf 4 5 6 7 8 9
| 7 = 47 [ ][ ]
Step 1 Find the quartiles.
The brackets group the values in the lower half and the values in the upper half.
The boxes are used to find the lower quartile and upper quartile.

12. Example 3 cont Step 2 Find the interquartile range.
The interquartile range is
Step 3 Find the outliers, if any.
An outlier must be 1.5(15) less than the lower quartile, 72, or 1.5(15) greater than the upper quartile, 87.
Answer: There are no values greater than Since 47 < 49.5, 47 is the only outlier.

13. Summary & Homework Summary: Homework:
The range of a data set is the difference between the greatest and the least values of the set and describes the spread of the data
The interquartile range is the difference between the upper and lower quartiles of a set of data. It is the range of the middle half of the data
Outliers are values that are much less than or much greater than the rest of the data
Homework:
pg 734; 12-23