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Standard XI

Mathematics

Standard Deviation about Mean

The mean and ...

Question

The mean and variance of n observations $x_{1}, x_{2}, x_{3}, . . . . . . . . . . . . . . x_{n}$ are $5$ and $0$ respectively. If $n \sum i = 1 x_{i}^{2} = 400$ , then n is

10

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Solution

The correct option is A $10$
$\sum_{i = 1}^{n} x_{i}^{2} = \frac{n (n + 1) (2 n + 1)}{6}$

Given,

$\sum_{i = 1}^{n} x_{i}^{2} = 400$

$400 = \frac{n (n + 1) (2 n + 1)}{6}$

$2400 = n (n + 1) (2 n + 1)$

$n (n + 1) (2 n + 1) = 2400$

$2 n^{3} + 3 n^{2} + n - 2400 = 0$

$F i n d o n e s o l u t i o n f o r 2 n^{3} + 3 n^{2} + n - 2400 = 0 u s i n g N e w t o n - R a p h s o n : n \approx 10.13443$

$∴ n = 10$

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