1. For same data, a process called coding makes computation of the mean easier. One kind of coding involves subtracting the same value from every score and then computing the mean of the residuals; then, the same value is added to the mean of the residuals to find the original score mean. To demonstrate coding:
a. Enter the following data into a MINITAB worksheet and complete the mean of these data in the ordinary manner:
1,010 1,024 1,036 1,029 1,045
1,020 1,027 1,027 1,031 1,037
1,047 1,018 1,032 1,024 1,029
b. Use MINITAB to generate a new column by subtracting 1,000 from each value, then compute the mean of the residuals. Then add the 1,000 to your computed value. Does this produce the same mean that you found in part a?
2. Fifty students took a chemistry exam and produced the list of scores given:
85 75 92 64 97 37 86 63 89 71
89 61 72 54 32 64 47 82 76 83
72 78 94 39 73 81 82 88 71 74
77 43 97 54 65 88 67 65 91 50
82 75 64 76 87 96 84 48 51 47
These scores are summarized in the grouped-data frequency distribution:
SCORES f
91-100 6
81-90 13
71-80 12
61-70 8
51-60 3
41-50 5
31-40 3
- Compute the grouped data mean for this distribution. Use MINITAB.
- Using the original scores, compute the raw-data mean. Use MINITAB.
- Explain why the grouped-data mean and raw-data are not exactly equal to each other.
3. Prepare a cumulative-relative frequency graph for the grouped-data test score distribution given in problem 2 above. From the graph, estimate this group's median score and compare it to the grouped-data mean. On the basis of this comparison, is the distribution skewed? Use MINITAB.