Further Mathematics Paper 2, Nov/Dec. 2014
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Main
Weakness/Remedies
Strength

Question 12

The table shows the frequency distribution of the ages of workers in a factory.

 Ages (years) Number of workers 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 40 – 44 45 – 49 50 – 54 55 – 59 60 - 64 5 22 30 32 25 36 32 30 21 2
1.  Using an assumed mean of 42, calculate, correct to one decimal place, the:

1. mean;
1. variance

of the distribution

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Observation

This question was reported to be very popular among the candidates and their performance was commended.  However, it was also observed that some candidates did not use the assumed mean as demanded by the rubrics of the paper.

Candidates were expected to obtain the following table.

 Ages F X d fd d2 fd2 15 - 19 5 17 -25 -125 625 3125 20 - 24 22 22 -20 -440 400 8800 25 - 29 30 27 -15 -450 225 6750 30 - 34 32 32 -10 -320 100 3200 35 - 39 25 37 -5 -125 25 625 40 - 44 36 42 0 0 0 0 45 - 49 32 47 5 160 25 800 50 - 54 30 52 10 300 100 3000 55 - 59 21 57 15 315 225 4725 60-  64 2 62 20 40 400 800 ∑f = 235 ∑fd = -645 ∑fd2 = 31825

Using the table, the mean was calculated using the formula, mean = A + , where A = Assumed mean = 42 i.e. Mean = 42 -  = 42 – 2.74 = 39.26
Variance was obtained by applying the formula   –  =   – ( = 127.89.