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Answer to Question #4347 in Statistics and Probability for Vetal Sangari

Question #4347
Q1. The following scores were obtained by 70 students in a Statistics Examinations
77 68 70 84 68 38 72 82 86 22
66 90 87 53 13 39 28 16 7 38
39 23 50 33 30 64 10 84 49 17
15 79 37 92 8 30 96 8 62 64
25 87 45 96 78 69 40 89 48 41
60 28 99 19 15 95 96 49 8 6
49 14 57 96 97 81 13 55 95 89
(a) Using Sturge’s Approximation, the number of classes K, of the above data is estimated to the nearest integer by the formula:
Use this to construct a grouped frequency distribution with the least lower limit of 5 for the data above.

(b) Draw a histogram for the distribution and use it to determine: (i) the mode
(ii) the three quartiles and hence an appropriate coefficient of skewness.

(c) Use the frequency distribution in (b) to calculate the:
(i) mean (ii) mode
(iii) median
(iv) standard deviation
(v) coefficient of variation
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