Let r be the range and ${S^2} = \frac{1}{{n - 1}}\mathop \sum \limits_{i = 1}^n {\left( {{x_i} - \bar x} \right)^2}$ be the S.D. of a set observations ${x_1},{x_2}, \ldots ,{x_n},$ then

$S = r\sqrt {\frac{n}{{n - 1}}} $

$S \ge r\sqrt {\frac{n}{{n - 1}}} $

JEE MATHEMATICS MCQ: STATISTICS

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Analyzing +4 | -1

Let r be the range and

{S^2} = \frac{1}{{n - 1}}\sum \limits_{i = 1}^n {\left( {{x_i} - \bar x} \right)^2}

be the S.D. of a set observations

{x_1},{x_2}, \ldots ,{x_n},

then

View answer and explanation

Correct option: A

S \le r\sqrt {\frac{n}{{n - 1}}}

Option A (

S \le r\sqrt {\frac{n}{{n - 1}}}

) is correct because it represents the relationship between the standard deviation (S) and the range (r) of a set of observations.

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