The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 resp

Question

The mean and S.D. 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 S.D. respectively are

Options:

A . 14.98, 39.95

B . 39.95, 14.98

C . 39.95, 224.5

D . None the these

Answer: Option B
:
B

Corrected \sum x = 40 \times 200 - 50 + 40 = 7990

∴ Corrected ¯ ¯ ¯ x = \frac{7990}{200} = 39.95

\sum x^{2} = n [σ^{2} + {¯ ¯ ¯ x}^{2}] = 200 [15^{2} + 40^{2}] = 365000

Correct \sum x^{2} = 365000 - 2500 + 1600 = 364100

∴ Corrected σ = \sqrt{\frac{364100}{200} - (39.95)^{2}}

= \sqrt{(1820.5 - 1596)} = \sqrt{224.5} = 14.98.

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