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JEE 2023 Mathematics PYQ — If the mean of the frequency distribution is 28, then its varianc… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

If the mean of the frequency distribution is 28, then its variance is _____.

Choose the correct answer:

A.
151
(Correct Answer)
B.
152
C.
153
D.
154

Correct Answer:

151

Explanation

$\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$
$28 = \frac{410 + 25 x}{14 + x} \Rightarrow x = 6$
$Variance = \frac{1}{N} \sum f_{i} x_{i}^{2} - (\overset{x}{ˉ})^{2}$

$Variance = \frac{1}{20} \times 18700 - (28)^{2} = 935 - 784 = 151$

Explanation

$\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$
$28 = \frac{410 + 25 x}{14 + x} \Rightarrow x = 6$
$Variance = \frac{1}{N} \sum f_{i} x_{i}^{2} - (\overset{x}{ˉ})^{2}$

$Variance = \frac{1}{20} \times 18700 - (28)^{2} = 935 - 784 = 151$

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