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Weighted average
Salary surveys often give a weighted average of the salary for a particular position. It is important to know that different surveys have different definitions of the term "weighted average."
Two definitions of "weighted average" that have been used in surveys are:
- The average weekly salary reported by a company for a given position multiplied by the number of employees in the job. The results are totaled for all companies reporting the position, and then divided by the total number of incumbents.
- The distribution of salaries is reviewed by deleting the top 25% and bottom 25% of the sample. The average is then computed from the interquartile range (this is also referred to as a trimmed mean).
The first definition is used by most surveys and will be taught in this section.
Weighted averages, as opposed to arithmetic or geometric means, provide results that represent the average of a total population, not just a subset of it. The results of weighting averages can be extrapolated to an entire population because they are closer to the true average of the population; whereas the results of arithmetic or geometric mean only represent the average of the subset of the population that they come from. The act of weighting the averages gives us the ability to compute an average that is representative of the entire population.
Example of weighted average. The pay rate for the position of Administrative Assistant from Company A and B are:
| Company | Pay Rate ($) | Incumbents |
|---|---|---|
| A | 20.00 | 6 |
| B | 18.50 | 2 |
What is the average pay for this position?
Weighted average solution. The average pay rate for the Administrative Assistant position at companies A and B using the arithmetic mean method is:
|
20.00 + 18.50 |
= 19.25 |
For the weighted average method, you need to account for the number of observations (incumbents) for the Administrative Assistant position at each company.
|
20.00 + 20.00 + 20.00 + 20.00 + 20.00 + 20.00 + 18.50 + 18.50 |
= 19.63 |
Alternatively,
|
20.00 (6) + 18.50 (2) |
= 19.63 |
The weighted average pay rate for the Administrative Assistant position for Company A and B is $19.63. This takes into account the average pay rate as weighted by the number of observations from Company A and the number of observations from Company B.
Memory Jogger
A survey reports the following for the position of Receptionist:
| Company | Salary ($) | Incumbents |
|---|---|---|
| A | 35,316 | 5 |
| B | 33,090 | 3 |
| C | 33,365 | 2 |
What is the average salary for the Receptionist position using the weighted average method?