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Question: In a series of 2n observations, half of them equal a and remaining half equal –a. If the standard de...

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

A

2n\frac{\sqrt{2}}{n}

B

2\sqrt{2}

C

2

D

1n\frac{1}{n}

Answer

2

Explanation

Solution

Let a, a, ..........n times – a, – a, – a, – a, ----- n time i.e. mean = 0 and S.D.=n(a−0)2+n(−a−0)22n= \sqrt{\frac{n(a - 0)^{2} + n( - a - 0)^{2}}{2n}}

2=na2+na22n=a2=±a2 = \sqrt{\frac{na^{2} + na^{2}}{2n}} = \sqrt{a^{2}} = \pm a. Hence ∣a∣ 6mu=2|a|\mspace{6mu} = 2