The following data relate to the pay of workers employed at a factory and the
average number of hours worked per week for June and November.
Type of worker Rate of pay June November Number of workers
Skilled K6.5 37 38.5 26
Semi-skilled K5.1 38.5 39.5 14
Unskilled K3.5 40.5 40 42
Required: Calculate a weighted aggregate index of average weekly pay for November
(June = 100), using the number of workers employed as a weighting factor.
To calculate a weighted aggregate index of average weekly pay for November, we need to follow these steps:
Step 1: Calculate the total pay for each type of worker in November
To calculate the total pay for each type of worker, we multiply the rate of pay by the average number of hours worked per week. Let's denote the rate of pay as "R", the average number of hours worked per week as "H", and the number of workers as "N".
For skilled workers:
Total pay for skilled workers in November = Rate of pay * Average number of hours worked per week * Number of workers
= K6.5 * 38.5 * 26
For semi-skilled workers:
Total pay for semi-skilled workers in November = Rate of pay * Average number of hours worked per week * Number of workers
= K5.1 * 39.5 * 14
For unskilled workers:
Total pay for unskilled workers in November = Rate of pay * Average number of hours worked per week * Number of workers
= K3.5 * 40 * 42
Step 2: Calculate the total pay for all workers in November
To calculate the total pay for all workers, we sum up the total pay for each type of worker.
Total pay for all workers in November = Total pay for skilled workers + Total pay for semi-skilled workers + Total pay for unskilled workers
Step 3: Calculate the weighted aggregate index of average weekly pay for November
The weighted aggregate index can be calculated by comparing the total pay for all workers in November to the total pay for all workers in June.
Weighted aggregate index of average weekly pay for November = (Total pay for all workers in November / Total pay for all workers in June) * 100
Now, you can substitute the values into the formulas to calculate the weighted aggregate index of average weekly pay for November.