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Let's say we have three employees. Their salary is 2000, 2500 and 6000 USD. Due to inflation each employee got an increase of 500 USD.
2000 -> 2500 USD: 25% increase.
2500 -> 3000 USD: 20% increase.
5000 -> 5500 USD: 10% increase.

Can HR department say the average salary increase was 18.33% by calculating (25+20+10)/3?

To me, averaging the percentages doesn't feel right here as the salaries are different at the beginning. I would argue the salary increased by 10% by calculating (5500+3000+2500)/(5000+3000+2000)=1.1

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    $\begingroup$ There are multiple ways to calculate it, depending on what exactly is the question. $\endgroup$
    – Tim
    Oct 12, 2022 at 15:20
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    $\begingroup$ There are strong arguments to avoid percentages in general because of such ambiguity. See this post by Frank Harrell, for example. $\endgroup$
    – EdM
    Oct 12, 2022 at 15:58
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    $\begingroup$ The equation at the end of the post has an error. It should be (5500+3000+2500)/(5000+2500+2000), which yields c. 16%. This is the same result as for ( sum(After) - sum(Before) ) / sum(Before). $\endgroup$ Oct 12, 2022 at 16:26
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    $\begingroup$ This setting forces you to recognize the fact that "average" is ambiguous. (There are infinitely many kinds of "averages" of numbers.) It would help, then, to explain what you want this average to represent or to tell us how you plan to use or interpret it. $\endgroup$
    – whuber
    Oct 12, 2022 at 16:39
  • $\begingroup$ Also, the question says, "Their salary is 2000, 2500 and 6000 USD", and then lists the salaries as 2000, 2500, and 5000. $\endgroup$ Oct 12, 2022 at 17:18

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As Tim mentions it depends on the question. I would argue that 18.33 percent increase is a more correct way of defining average salary increase from the employees point of view.

The percentage increase in salary expenses, 10 percent, would probably be more correct to present to management regarding how much you spent on employeers salaries.

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  • $\begingroup$ +1, with the caveat that the correct result from the management perspective is c. 15.8% $\endgroup$ Oct 12, 2022 at 16:28

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