# 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

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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