Let xi(1≤i≤10) be ten observations of a random variable  X. If ∑i=110 xi−p=3 and ∑i=110 xi−p2=9, where0≠p∈R, then the standard deviation of these observations is

# Let ${x}_{i}\left(1\le i\le 10\right)$ be ten observations of a random variable , where$0\ne p\in R,$ then the standard deviation of these observations is

1. A

$\frac{4}{5}$

2. B

$\sqrt{\frac{3}{5}}$

3. C

$\frac{9}{10}$

4. D

$\frac{7}{10}$

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### Solution:

Let ${\sigma }_{X}$ be the standard deviation. Then,

It follows from the above discussion that in case of individual observations, variance/ standard deviation may be computed by applying any of the above three formulas. In order to calculate the variance when deviations are taken from the actual mean, we may use the following algorithm.

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