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                  | Question 7
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                  | 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: 
                      mean;variance              of the numbers. |  
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                    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. |  
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