First slide

Introduction to statistics

Question

In a series of 2n observations, half of them equal a and remaining half equal –a. if the standard deviation of the observation is 2, then $| a |$ equals.

Moderate

A

$\frac{\sqrt{2}}{n}$
B

$\sqrt{2}$
C

2
D

$\frac{1}{n}$

Solution

Clearly mean A = 0
Standard deviation $σ = \sqrt{\frac{\sum {(x - A)}^{2}}{2 n}}$

$2 = \sqrt{\frac{{(a - 0)}^{2} + {(a - 0)}^{2} + {(0 - a)}^{2} + ........}{2 n}}$

$= \sqrt{\frac{a^{2} .2 n}{2 n}} = | a |$

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