While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Question

Philoid · Accepted Answer

Given, Uncorrected mean is 40 and corrected SD is 10 and N = 100

To Find: Find the correct mean and SD

Explanation: Here,

Then,

The corrected sum of observation

So,

Variance =16

Incorrect

Correct

Correct SD,

SD = 6.62

Variance = 6.62×6.62

Hence, Variance = 43.82