Further Mathematics Paper 2 WASSCE private candidates second series 2019

Question 6

The table shows the distribution of wages earned by employees in a company.



Wages ($) 40 – 49 50 – 59 60 – 69 70 – 79 80 – 89 90 – 99 100 – 109 110 – 119
Number of
Employees
4 12 14 11 7 5 2 1

Using an assumed mean of $74.50, find the mean wage.

Observation

The Chief Examiner reported some of the candidates that attempted this question did not make use of the formula for assumed mean and some others that did, could not express their answer in monetary unit and hence lost the mark for the final answer.


Wages ($) f x d = x – 44.5 fd
40 – 49 4 44.5 -30 -120
5059 12 54.5 -20 -240
60-69 14 64.5 -10 -140
70-79 11 74.5 0 0
80-89 7 84.5 10 70
90-99 5 94.5 20 100
100-109 2 104.5 30 60
110-119 1 114.5 40 40
Total 56 -230

Mean wage = A + ∑𝑓𝑑𝑓, where A is the assumed mean = 74.5. Then, substituting into the
formula to obtain mean wage = 74.5 + (−23056) = 74.5 – 4.11 = $70.39.