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# chapter3 - Chapter 3 Numerically Describing Data from One...

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121 Chapter 3 Numerically Describing Data from One Variable 3.1 Measures of Central Tendency 1. A statistic is resistant if it is not sensitive to extreme data values. The median is resistant because it is a positional measure of central tendency and increasing the largest value or decreasing the smallest value does not affect the position of the center. The mean is not resistant because it is a function of the sum of the data values. Changing the magnitude of one value changes the sum of the values, and thus affects the mean. The mode is a resistant measure of center. 2. The men and the median are approximately equal when the data are symmetric. If the mean is significantly greater than the median, the data are skewed right. If the mean is significantly less than the median, the data are skewed left. 3. Since the distribution of household incomes in the United States is skewed to the right, the mean is greater than the median. Thus, the mean household income is \$55,263 and the median is \$41,349. 4. HUD uses the median because the data are skewed. Explanations will vary. One possibility is that the price of homes has a distribution that is skewed to the right, so the median is more representative of the typical price of a home. 5. The mean will be larger because it will be influenced by the extreme data values that are to the right end (or high end) of the distribution. 6. 10,000 1 5000.5 2 + = . The median is between the 5000 th and the 5001 st ordered values. 7. The mode is used with qualitative data because the computations involved with the mean and median make no sense for qualitative data. 8. parameter; statistic 9. False. A data set may have multiple modes, or it may have no mode at all. 10. False. The formula 1 2 n + gives the position of the median, not the value of the median. 11. 20 13 4 8 10 55 11 55 x ++++ == = 12. 83 65 91 87 84 420 84 x = 13. 3 6 10 12 14 45 9 μ =

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Chapter 3 Numerically Summarizing Data 122 14. 11 92 51 21 62 81 36 1 3 5 15 99 μ ++++++++ == = 15. 142 2.4 59 . The mean price per ad slot is approximately \$2.4 million. 16. Let x represent the missing value. Since there are 6 data values in the list, the median 26.5 is between the 3 rd and 4 th ordered values which are 21 and x , respectively. Thus, 21 26.5 2 21 53 32 x x x + = += = The missing value is 32. 17. 420 462 409 236 1527 Mean \$381.75 44 +++ = Data in order: 236, 409, 420, 462 409 420 829 Median \$414.50 22 + = No data value occurs more than once so there is no mode. 18. 35.34 42.09 39.43 38.93 43.39 49.26 248.44 Mean \$41.41 66 +++++ Data in order: 35.34, 38.93, 39.43, 42.09, 43.39, 49.26 39.43 42.09 81.52 Median \$40.76 + = No data value occurs more than once so there is no mode. 19. 3960 4090 3200 3100 2940 3830 4090 4040 3780 33,030 Mean 3670 psi = Data in order: 2940, 3100, 3200, 3780, 3830, 3960, 4040, 4090, 4090 Median = the 5 th ordered data value = 3830 psi Mode = 4090 psi (because it is the only data value to occur twice) 20. 282 270 260 266 257 260 267 1862 Mean 266 minutes 77 ++++++ = Data in order: 257, 260, 260, 266, 267, 270, 282 Median = the 4 th data value with the data in order = 266 minutes Mode = 260 minutes (because it is the only data value to occur twice) 21. (a) The histogram is skewed to the right, suggesting that the mean is greater than the median. That is, x M > .
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chapter3 - Chapter 3 Numerically Describing Data from One...

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