The mean and standard deviation of the marks of 20 students were found to be 40 and 15 respectively. Later, it was discovered that a score of 60 was wrongly read as 40, then the correct variance will be

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The mean and standard deviation of the marks of 20 students were found to be 40 and 15 respectively. Later, it was discovered that a score of 60 was wrongly read as 40, then the correct variance will be

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232

236

240

244

answer is D.

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Detailed Solution

Corrected mean

= 800 − 40 + 60 20 = 41

In correct

S D = ∑ x 12 20 − ∑ x 1 n 2

⇒ ∑ x 12 = 20 [225 + 1600] = 36500

⇒ corrected sum = 36500 − 402 + 602 = 38500

∴ Variance = 3850020 − (41) 2 = 1925 − 1681 = 244

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