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 Further Mathematics Paper 2, Nov/Dec. 2013
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 7

The deviations of 85 from some numbers are -6, -4, -2, 1, 2, 3, 4, 5 and 8.  Find, correct to two decimal places, the:

1. mean;
2. variance

of the numbers.

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Observation

It was reported that this question was attempted by majority of the candidates and they performed well in it.  It was also observed that majority of the candidates did not use the method of assumed mean but rather derived the numbers using the given deviations before calculating the mean and variance.  The disadvantage of using this method was that it was longer and the values that would be obtained were bigger and more difficult to manipulate.  Candidates were expected to find the mean by calculating the mean of the deviation and add the result to 85 i.e. Mean = 85 + .  ∑d = -6 + (-4) + (-2) + 1 + 2 + 3 + 4 + 5 + 8 = 11.  Therefore mean = 85 +  = 86.22.  ∑d2 = (-6)2 + (-4)2 + (-2)2 + 12 + 22 + 32 + 42 + 52 + 82 = 175.  Variance =   =    ²  =  = 17.95.