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 \left | a \right | equals

  • Option 1)

    2

  • Option 2)

    \sqrt{2}

  • Option 3)

    \frac{1}{n}

  • Option 4)

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

 

Answers (1)

As we learnt in

Standard Deviation -

If x1, x2...xn are n observations then square root of the arithmetic mean of 

\sigma = \sqrt{\frac{\sum \left ( x_{i}-\bar{x} \right )^{2}}{n}}

\bar{}

- wherein

where \bar{x} is mean

 

 Standard deviation =\sqrt{\frac{\sum (x-\bar{x})^2}{N}}\ \: \: \, \, \, \, \, \, \, \, where \:\bar{x}=mean,N= No. \: of\: observation

Here,\bar{x}=\frac{(a+a+a..)n\:times-(a+a+a......n \:times)}{2n}=\:0

N = 2n

Hence standard deviation=\sqrt{\frac{\sum x^2}{2n}}


Option 1)

2

Correct

Option 2)

\sqrt{2}

Incorrect

Option 3)

\frac{1}{n}

Incorrect

Option 4)

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

Incorrect

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