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 + ∑𝑓𝑑⁄∑𝑓, where A is the assumed mean = 74.5. Then, substituting into the
formula to obtain mean wage = 74.5 + (−230⁄56) = 74.5 – 4.11 = $70.39.