Descriptive Statistics

Question

A group of ten numbers has a recorded mean of fifteen, but later one entry originally read as eight is found to be twenty-three; what is the corrected mean of the ten numbers?

RankGuru · Accepted Answer

The mean equals the total sum divided by the number of observations, so any correction to a single value changes the sum by the difference and shifts the mean by that difference spread over all entries. This sum-adjustment idea is a routine JEE Advanced descriptive-statistics manoeuvre. The original total of ten numbers is mean × count = 15 × 10 = 150. The wrong entry 8 must be replaced by the correct value 23, increasing the sum by 23 − 8 = 15, giving a corrected total of 150 + 15 = 165. Dividing by 10 yields the corrected mean 165/10 = 16.5. Option 16.0 results from adding only 10 instead of the true difference 15. Option 15.5 comes from spreading half the correction. Option 17.0 over-adds by using a difference of 20. The principle is that the mean responds linearly to the corrected sum, here total/count. Plausibility check: replacing 8 by the larger 23 must raise the mean, and the increase of 1.5 equals the correction 15 divided by the 10 observations, exactly as the averaging mechanism predicts.

Descriptive Statistics

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