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Homework - Central Tendency & Variability

DIRECTIONS: When computation is required, be sure to show all work neatly (i.e., each and every step as indicated in the class examples given). Attach Minitab output when the problem requests it. Indicate on the output whether the values agree with what you have calculated by hand.

Problems

  1. Compute the mean, range, mean deviation, variance, and standard deviation for the following sample data. Compute the standard deviation using the definitional formula and then again using the computational formula. The idea is for you to see how much easier the computational formula is to use than the definitional formula. When you are through with the manual computations, use Minitab to do them. The data represent the number of fish caught while ice fishing for 10 people (30 points).
    9, 7, 5, 8, 6, 3, 0, 6, 6, 1.
  2. Compute the mean, range, mean deviation, variance, and standard deviation for the following sample data. Compute the standard deviation using the definitional formula and then again using the computational formula. The idea is for you to see how much easier the computational formula is to use than the definitional formula. When you are through with the manual computations, use Minitab to do them. The data represent the average number hours of sleep per night for a bunch of teenagers (30 points).
    5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11.
  3. Compute the mean and standard deviation for the following by whatever manual method you prefer, and then use Minitab to do them. The data represent hypothetical scores on an exam for a sample of students (30 points).
    63 88 79 92 86 87 83 78 41 67
    68 76 46 81 92 77 84 76 70 66
    77 75 98 81 82 81 87 78 80 60
    94 79 52 82 77 61 77 70 74 61

Multiple Choice (10 points)

  1. Which measure of central tendency is the MOST sensitive to extreme scores?
    a. mean
    b. median
    c. mode
    d. trimmed mean
    e. variance

  2. Suppose the mean of our first exam is 77 and the median is 82. This would indicate a _____ distribution.
    a. normal
    b. bimodal
    c. rectangular
    d. positively skewed
    e. negatively skewed

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