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Measures of Variation For Example: The 11 Workers at a company have the following ages: 27, 39, 40, 22, 19, 25, 41, 58, 53, 49, 51 Order data from least.

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Presentation on theme: "Measures of Variation For Example: The 11 Workers at a company have the following ages: 27, 39, 40, 22, 19, 25, 41, 58, 53, 49, 51 Order data from least."— Presentation transcript:

1 Measures of Variation For Example: The 11 Workers at a company have the following ages: 27, 39, 40, 22, 19, 25, 41, 58, 53, 49, 51 Order data from least to greatest: 19, 22, 25, 27, 39, 40, 41, 49, 51, 53, 58 First Quartile or lower quartile is the median of the lower half of the data. Second Quartile is the median of the data set. Third Quartile or upper quartile is the median of the upper half of the data. First Quartile Third Quartile Second Quartile (median) Another way to use statistics to analyze data is to measure how a data set is spread out. These statistics are called Measures of Variation. Measures of Variation

2 Example 1 Find the quartiles for the data set below. 7, 9, 10, 11, 11, 12, 12, 13, 14, 16, 16 First Quartile (lower) Second Quartile (median) Third Quartile (upper) Range is the difference between the greatest and least values in a data set. More Measures of Variation Interquartile Range is the range in the middle of the data. It is the difference between the upper and lower quartiles in a data set. Range 16 – 7 = 9 Interquartile Range 14 – 10 = 4

3 Example 2 In his 21 major league seasons, Cal Ripken hit the following number of home runs: 0, 28, 27, 27, 26, 25, 27, 23, 21, 21, 34, 14, 24, 13, 17, 26, 17, 14, 18, 15, 14 Find the range and interquartile range.

4 Example 2 In his 21 major league seasons, Cal Ripken hit the following number of home runs: 0, 28, 27, 27, 26, 25, 27, 23, 21, 21, 34, 14, 24, 13, 17, 26, 17, 14, 18, 15, 14 Find the range and interquartile range. Order data from least to greatest. 0, 13, 14, 14, 14, 15, 17, 17, 18, 21, 21, 23, 24, 25, 26, 26, 27, 27, 27, 28, 34

5 Example 2 In his 21 major league seasons, Cal Ripken hit the following number of home runs: 0, 28, 27, 27, 26, 25, 27, 23, 21, 21, 34, 14, 24, 13, 17, 26, 17, 14, 18, 15, 14 Find the range and interquartile range. Order data from least to greatest. 0, 13, 14, 14, 14, 15, 17, 17, 18, 21, 21, 23, 24, 25, 26, 26, 27, 27, 27, 28, 34 Range 34 – 0 = 34 First Quartile (lower) Second Quartile (median) Third Quartile (upper) 14.5 26.5 Interquartile Range 26.5 – 14.5 = 12.0

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