Lesson 13-4

Measures of Variation

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

Objectives

• Find the range of a set of data

• Find the quartiles and the Interquartile range of a set of data

Vocabulary

• range – • measures of variation – • quartiles – • lower quartile – • upper quartile – • Interquartile range – • outlier –

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

biggestsmallestQ1 Q2 Q325% 25% 25% 25%

Range

Interquartile Range

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 ForceBoise St.ClemsonFlorida St.Georgia TechIdahoIndianaKentuckyMiamiMichiganNebraskaNorthwesternPurdueTexasTulane

497154594911658847894985483049005069490050595232518348254989

The greatest amount of yardage gains is 6588, and the least amount of yardage gains is 4789.

Answer: The range of theyardage isor 1799 yards.

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.

StateArea (thousand square miles)

AlaskaCaliforniaMontanaNew MexicoTexas

656164147124269

Explore You are given a table with the areas of the 5largest states. You are asked to find the median,the lower quartile, the upper quartile, and theinterquartile range.

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 theinterquartile range.

124 147 164 269 656

Solve median

Example 2 cont

Answer: The median is 164 thousand square miles.

Examine Check to make sure that the numbers are listed in order. Since 135.5, 164, and 462.5 divide the data into four equal parts, the lower quartile, median, and upper quartile are correct.

The lower quartile is 135.5 thousand square miles and the upper quartile is 462.5 thousand square miles.

The interquartile range is 462.5 – 135.5 or 327 thousand square miles.

Example 3Identify any outliers in the following set of data.

Stem Leaf

456789

7891 2 2 3 5 6 6 7 82 5 7 7 90 3 8 4 | 7 = 47

Step 1 Find the quartiles.The brackets group the values in the lower half and the values in the upper half.

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]

The boxes are used to find the lower quartile and upper quartile.

Example 3 cont

Step 2 Find the interquartile range.

An outlier must be 1.5(15) less than the lower quartile, 72, or 1.5(15) greater than the upper quartile, 87.

The interquartile range is

Step 3 Find the outliers, if any.

Answer: There are no values greater than 109.5. Since 47 < 49.5, 47 is the only outlier.

Summary & Homework

• Summary:– 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