Math CentralQuandaries & Queries


Question from Cavell:

Hi, the projected cost was 71,700. The actual cost was 56,876. What is the percent difference?


Hi Cavell,

The difference is 71,700 - 56,876 = 14,824. But you want the difference presented as a percentage. The difficulty is that when you say percentage you should say "percentage of what".

14,824 as a percentage of the projected cost is

14824/71700 × 100 = 20.7%

14,824 as a percentage of the actual cost is

14824/56876 × 100 = 26.1%

An unambiguous way to express what happened is to represent the actual cost as a percentage of the projected cost.

56876/71700 × 100 = 79.3%

and say

The actual cost was 79.3% of the projected cost.

The difference is then, 100% - 79.3% = 20.7%, and the "percentage of what?" question is clearly answered by the way you have reported situation in the statement above.

I hope this helps,

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