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The mean and S.D of the marks of 200 candiditaes 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

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14.98, 39.95

39.95, 224.5

39.95, 14.98

39.00, 14.00

answer is B.

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Detailed Solution

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

$∴$ Correct $\bar{x} = 7990 / 200 = 39.95$
Incorrect

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

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

$∴$ Corrected

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

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