Main Idea and New Vocabulary Key Concept: Measures of Variation Example 1: Find Measures of Variation Example 2: Find Outliers Example 3: Analyze Data Lesson Menu

Find the measures of variation of a set of data. range quartile lower quartile upper quartile interquartile range outlier Main Idea/Vocabulary

Key Concept

Find Measures of Variation OLYMPICS Find the measures of variation for the data in the table. Range 110 – 25 or 85 medals Example 1

Find Measures of Variation Quartiles Order the numbers from least to greatest. 25 41 46 72 100 110 lower half median upper half LQ UQ Interqartile Range 100 – 41 or 59 UQ – LQ Example 1

Find Measures of Variation Answer: The range is 85, the median is 59, the lower quartile is 41, the upper quartile is 100, and the interquartile range is 59. Example 1

Find the measures of variation for the data in the table. A. range: 96.3; median: 95.5; lower quartile: 84; upper quartile: 101; interquartile range: 17 B. range: 38; median: 95.5; lower quartile: 84; upper quartile: 101; interquartile range: 27 C. range: 38; median: 95.5; lower quartile: 84; upper quartile: 101; interquartile range: 17 D. range: 38; median: 93; lower quartile: 82; upper quartile: 98; interquartile range: 17 Example 1 CYP

Order the numbers from least to greatest. 71, 89, 90, 92, 92, 94, 95 Find Outliers TEMPERATURES The average daily temperatures in degrees Fahrenheit for one week in July were 94, 92, 90, 95, 71, 89, and 92. Name any outliers in the data. Order the numbers from least to greatest. 71, 89, 90, 92, 92, 94, 95 The lower quartile is 89 and the upper quartile is 94. Find the interquartile range. 94 – 89 = 5 Multiply the interquartile range by 1.5. 5 × 1.5 = 7.5 Example 2

Find Outliers Subtract 7.5 from the lower quartile and add 7.5 to the upper quartile. 89 – 7.5 = 81.5 94 + 7.5 = 101.5 The limits for outliers are between 81.5 and 101.5. The only outlier in the data set is 71. Answer: 71 Example 2

The test scores of the students in Mr The test scores of the students in Mr. Pete’s math class are 87, 81, 61, 88 90, 99, 94, 92, 90, and 85. Name any outliers in the data. A. 61 B. 61 and 81 C. 99 D. no outliers Example 2 CYP

Find the measures of variation for both classes. Analyze Data DANCE The table shows the ages of students in two different classes at a dance studio. Compare and contrast the measures of variation. Find the measures of variation for both classes. Example 3

Analyze Data Ballet Hip Hop Range 18 – 15 or 3 15 – 12 or 3 Median 16.5 13 UQ 17 14 LQ 16 13 Interquartile Range 17 – 16 or 1 14 – 13 or 1 Answer: Both classes have a range of 3 and an interquartile range of 1. The lower quartile, median, and upper quartile of the ballet class are all greater than those of the hip hop class. Example 3

A. All measures are higher for Corn Type I. CORN The table shows the length, in inches, of the stalks of two types of corn that Myra had planted in her garden. Compare and contrast the measures of variation. Which statement is true? A. All measures are higher for Corn Type I. B. All measures are higher for Corn Type II. C. The range is the same for both. All other measures are higher for Corn Type I. D. The median and range is higher for Corn Type I. All other measures are higher for Corn Type II. Example 3 CYP