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CHAPTER 4
SOLUTIONS TO PROBLEMS

  1. The mean is equal to:

    The median is the average of the 10th and 11th scores in the rank ordered frequency distribution:

    The median is the preferred measure of central tendency for these data. The value of the mean is inflated by the existence of two extremely large scores (88, 112). The mean value of almost 17 crimes per addict exaggerates the central tendenc y, or "most typical" score.

  2. The most appropriate measure of central tendency for this data is the mode, because the data are measured at the nominal level. The modal or "most typical" reason for requesting the police is for "Other Reasons". Thi s finding suggests that the police may spend a good part of their time responding to calls that may not concern crimes or other "police work".

  3. The mode is the interval 30% - 39%, since this interval has the highest frequency (38). The median is:

    The mean is found by multiplying the midpoint of each interval by the interval's frequency, and dividing by the total number of scores:

  4. Weighted mean:

  5. Mean number of executions:

    Median number of executions is equal to 1.

    When executions for the year 1984 (21) are added to the data, the mean becomes:

    The median becomes 1.5 executions. The median is the more appropriate measure of central tendency for the 1977-1984 data distribution because it is less affected by the inclusion of the 1984 data than the mean. When the 1984 data are include d, the mean number of executions increases from 1.57 to 4, while the median increases from 1 to 1.5. One and one-half executions per year seems to describe the 1977-1984 data distribution better.

  6. The weighted mean for this data can be determined by:

  7. The mean is obtained by multiplying the midpoint of each interval by its frequency:

    The median is:

    The mode is equal to the interval 3 - 5 times because it contains the highest frequency (87).

  8. The mean is equal to:

    The median is equal to 69.5.

    The mean and the median are very comparable to one another, this would suggest that there are no or few extreme scores in the data, that the data are not skewed.



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Copyright ©2001 The McGraw-Hill Companies.
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