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------------------------------------------------ A student obtained the mean and the standard deviation of 100 observations as 40 and 5.1. It was later found that one observation was wrongly copied as 50, the correct figure being 40.

Find the correct mean and standard deviation:

A. Mean = 38.8, S.D. = 5
B. Mean = 39.9, S.D. = 5
C. Mean = 39.9, S.D. = 4
D. None of the above

To find the correct mean and standard deviation, adjust the sum of observations and sum of squares. The correct mean is 38.8 and the correct standard deviation is 5.0.

Explanation:

The question asked is: A student obtained the mean and the standard deviation of 100 observations as 40 and 5.1. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and the S.D. a. mean 38.8, S.D = 5 b. mean = 39.9, S.D = 5 c. mean = 39.9, S.D = 4 d. none

To find the correct mean and standard deviation, we need to adjust for the wrongly copied observation. Since one observation was incorrectly recorded as 50 instead of 40, we need to subtract 10 from the sum of the observations. The correct mean will be obtained by dividing the adjusted sum by 100. The correct standard deviation can be found by adjusting the sum of squares of the observations and then dividing by 100.

The correct mean is 38.8 and the correct standard deviation is 5.0.

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