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Question 5
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The deviations of the set of numbers from 55 are -5, -3, -1, 0, 1, 3, 5 and 7
Calculate the:
(a) mean of the numbers.
(b) variance of the numbers
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This question was well attempted by most candidates. It was observed that candidates preferred the raw score method, which takes a longer time, to the deviation method. This perhaps may be due to the lack of understanding of the deviation method. They were expected to apply the formula:
(a) mean = A+Sd where A = assumed mean, d = deviations from the assumed mean (given) and n = number of deviations n which gives mean = 55 + 7/8 = 58.875.
(b) Variance = Sd2 - Sd 2
n n where, d = deviations, d = mean of the deviations and n = number of deviations
which gives = Sd2 = 25 + 9 + 1 + 1 + 9 = 25 + 49 = 119
variance = 119 - 49 = 14.875 - 0.7656 = 14.11 to 2 decimal places
8
64
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