Prentice Hall Algebra 1

Chapter 12 Data Analysis and Probability > 12-3 Measures of Central Tendency and Dispersion

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1. The grades in Problem 2 were 80, 93, and 91. What grade would you need on your next exam to have an average of 88 on the four exams?
2. Reasoning If 100 is the highest possible score on the fourth exam, is it possible to raise your average to 92? Explain.

A measure of dispersion describes how dispersed, or spread out, the values in a data set are. One measure of dispersion is range. The range of a set of data is the difference between the greatest and least data values.

Problem 3 Finding the Range

Finance The closing prices, in dollars, of two stocks for the first five days in February are shown below. What are the range and mean of each set of data? Use the results to compare the data sets.

Stock A: 25 30 30 47 28	Stock B: 34 28 31 36 31
range: 47 minus 25 equals 22	range: 36 minus 28 equals 8
mean: 25 + 30 + 30 + 47 + 28 5 = 160 5 = 32 table with 2 rows and 1 column , row1 column 1 , fraction 25 plus 30 plus 30 plus 47 plus 28 , over 5 end fraction , row2 column 1 , equals , 160 over 5 , equals 32 , end table	mean: 34 + 28 + 31 + 36 + 31 5 = 160 5 = 32 table with 2 rows and 1 column , row1 column 1 , fraction 34 plus 28 plus 31 plus 36 plus 31 , over 5 end fraction , row2 column 1 , equals , 160 over 5 , equals 32 , end table

Both sets of stock prices have a mean of 32. The range of the prices for Stock A is 22, and the range of the prices for Stock B is 8. Both stocks had the same average price during the 5-day period, but the prices for Stock A were more spread out.

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For the same days, the closing prices, in dollars, of Stock C were 7, 4, 3, 6, and 1. The closing prices, in dollars, of Stock D were 24, 15, 2, 10, and 5. What are the range and mean of each set of data? Use your results to compare Stock C with Stock D.

Adding the same amount to each value in a set of data has special consequences for the mean, median, mode, and range.

Consider the data set 5, 16, 3, 5, 11.

mean: 8

median: 5

mode: 5

range: 13

If you add 5 to each data value, you get the data set 10, 21, 8, 10, 16.

mean: 13

median: 10

mode: 10

range: 13

Notice that the mean, median, and mode all increased by 5. The range did not change. For any data set, if you add the same amount k to each item, the mean, median, and mode of the new data set also increase by k. The range does not change.

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Problem 3 Finding the Range

Think

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