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Question

The mean and standard deviation of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40 was wrongly read as 50. The correct mean and standard deviation respectively are:

A
14.98, 39.95
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B
39.95, 14.98
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C
39.95, 224.5
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D
None the these
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Solution

The correct option is B 39.95, 14.98
Corrected x=40×20050+40=7990
Corrected ¯¯¯x=7990200=39.95
x2=n[σ2+¯¯¯x2]=200[152+402]=365000
Correct x2=3650002500+1600=364100
Corrected σ=364100200(39.95)2
=(1820.51596)=224.5=14.98.

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