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Question:

A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is?

10√(3)

100√(3)

1303

103

Solution:

Correct option is A. 10√(3)
Let x be the 6th observation
⇒ 45 + 54 + 41 + 57 + 43 + x = 48 × 6 = 288
⇒ x = 48
Variance = (Σ x_i^2/6 - (x̄)^2) ⇒ variance = 14024/6 - (48)^2 = 1003
⇒ standard deviation = 10√(3)