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Calculating Measures of Data Sets: Mean, Median, Mode, Range

This text explains how to compute the mean, median, mode, and range of a data set. It provides examples and definitions for each measure.

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Calculating Measures of Data Sets: Mean, Median, Mode, Range

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  1. California Standards SDAP1.1 Compute the range, mean, median, and mode of data sets.

  2. Vocabulary mean median mode range

  3. Players on a volleyball team measured how high they could jump. The results in inches are recorded in the table. One way to describe this data set is to find the mean. The mean is the sum of all the items divided by the number of items in the set. Sometimes the mean is also called the average.

  4. Additional Example 1A: Finding the Mean of a Data Set Find the mean of each data set. 5 + 8 + 3 + 5 + 4 + 2 + 1 = 28 28 ÷ 7 = 4 Add all values. Divide the sum by the number of items. The mean is 4 inches.

  5. Additional Example 1B: Finding the Mean of a Data Set Find the mean of each data set. 96 + 75 + 84 + 7 = 262 262 ÷ 4 = 65.5 Add all values. Divide the sum by the number of items. The mean is 65.5 points. The average number of points scored is 65.5.

  6. Check It Out! Example 1A Find the mean of each data set. Add all values. 1 + 2 + 10 + 2 + 5 + 6 + 9 = 35 35 ÷ 7 = 5 Divide the sum by the number of items. The mean is 5 inches.

  7. Check It Out! Example 1B Find the mean of each data set. 53 + 26 + 47 + 12 = 138 138 ÷ 4 = 34.5 Add all values. Divide the sum by the number of items. The mean is 34.5 points. The average number of points scored is 34.5.

  8. Some other descriptions of a set of data are called the median, mode, and range. • The median is the middle value when the data are in numerical order, or the mean of the two middle values if there are an even number of items. • The mode is the value or values that occur most often. There may be more than one mode for a data set. When all values occur an equal number of times, the data set has no mode. • The range is the difference between the least and greatest values in the set.

  9. mean:12 + 11 + 14 + 15 12 + 14 4 2 Additional Example 2: Finding the Mean, Median, Mode, and Range of a Data Set Find the mean, median, mode, and range of the data set. Add all the values. Divide the sum by the number of items. = 13 median: 11, 12, 14, 15 Write the data in numerical order: 11, 12, 14, 15. There are an even number of items, so find the mean of the two middle values. = 13 No value occurs most often. mode: none Subtract the least value from the greatest value. range: 15 – 11 = 4 The mean is 13 cars washed; the median is 13 cars washed; there is no mode; and the range is 4 cars washed.

  10. mean:17 + 11 + 22 + 14 14 + 17 4 2 Check It Out! Example 2 Find the mean, median, mode, and range of the data set. Add all the values. Divide the sum by the number of items. = 16 median: 11, 14, 17, 22 Write the data in numerical order: 11, 14, 17, 22.There are an even number of items, so find the mean of the two middle values. = 15.5 mode: none No value occurs most often. Subtract the least value from the greatest value. range: 22 – 11 = 11 The mean is $16; the median is $15.50; there is no mode; and the range is $11.

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