Let x _ i (1 i 10) be ten observations of a random variable X . I… - Vidyadip

MCQ

Let $x _{ i }(1 \leq i \leq 10)$ be ten observations of a random variable $X .$ If $\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)=3$ and $\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)^{2}=9$ where $0 \neq p \in R ,$ then the standard deviation of these observations is

A
$\sqrt{\frac{3}{5}}$
B
$\frac{7}{10}$
✓
$\frac{9}{10}$
D
$\frac{4}{5}$

✓

Answer

Correct option: C.

$\frac{9}{10}$

c
Variance $=\frac{\sum\left( x _{ i }- p \right)^{2}}{ n }-\left(\frac{\sum\left( x _{ i }- p \right)}{ n }\right)^{2}$

$=\frac{9}{10}-\left(\frac{3}{10}\right)^{2}=\frac{81}{100}$

$S.D. =\frac{9}{10}$

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