12-3 Measures of Central Tendency and Dispersion

Quick Review

The mean of a data set equals sum of the data values total number of data values . fraction sumofthedatavalues , over totalnumberofdatavalues end fraction . .  The median is the middle value in the data set when the values are arranged in order. The mode is the data item that occurs the most times. The range of a set of data is the difference between the greatest and least data values.

Example

The quality ratings of 9 movies showing at a movie theater near you are 5.6, 7.9, 7.0, 5.9, 7.8, 6.2, 6.4, 5.2, and 5.6. What are the mean, median, mode, and range of the data?

mean:

5.6 + 7.9 + 7.0 + 5.9 + 7.8 + 6.2 + 6.4 + 5.2 + 5.6 9 = 6.2 fraction 5.6 plus 7.9 plus 7.0 plus 5.9 plus 7.8 plus 6.2 plus 6.4 plus 5.2 plus 5.6 , over 9 end fraction . equals 6.2

Exercises

Find the mean, median, mode, and range of each data set.

12. points scored by a football team: 23 31 26 27 25 28 23 23 25 29 29 29 25 22 30
13. clips per package: 12 12 13 12 12 12 12 12 12 13 12 11 12 12 12 12 12
14. Cats A veterinarian examines 9 cats. The weights of the cats are 13.4 lb, 13.1 lb, 10.4 lb, 6.8 lb, 11.4 lb, 10.8 lb, 13.4 lb, 11.3 lb, and 9.3 lb. Find the mean, median, and mode of the data. Which measure of central tendency best describes the data?
15. Basketball A basketball player scores 22, 19, 25, and 17 points in four games. How many points does the basketball player need to score in the fifth game to average 22 points scored per game?

12-4 Box-and-Whisker Plots

Quick Review

A box-and-whisker plot organizes data values into four groups using the minimum value, the first quartile, the median, the third quartile, and the maximum value.

Example

What box-and-whisker plot represents the test scores below?

62 57 78 69 85 43 94 82 61 90 83 51 67 88 55

Arrange the data in order from least to greatest.

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Exercises

Make a box-and-whisker plot of each data set.

16. movie lengths (min):

    125 117 174 131 142 108 188 162 155 167 129 133 147 175 150

17. dog weights (lb):

    23 15 88 34 33 49 52 67 42 71 28

18. book lengths (pages):

    178 223 198 376 284 156 245 202 315 266

19. Which box-and-whisker plot represents the data set with the greater interquartile range? Explain.
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