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InterviewSolution
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In a series of 2n observation, half of them equal 'a' and remaining half equal '-a'.If the standard deviation of the observations is 2,then find the value of |a|. |
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Answer» Given, N = 2a, Mean, \(\bar{x}=\frac{a+a+...+a+(-a)+(-a)+...(-a)}{2n}\) \(=\frac{0}{2n}\) = 0 Standard deviation, ⇒ \(σ^2=2^2\) \(⇒\frac{\displaystyle\sum {x_i}^2}{N}-(\frac{\displaystyle\sum {x_i}}{N})^2=4\) \(⇒\frac{\displaystyle\sum {x_i}^2}{N}-x^{-2}=4\) \(⇒\frac{\displaystyle\sum {x_i}^2}{N}-0=4\) \(⇒\displaystyle\sum {x_i}^2=8n\) ⇒ a2 + a2 + ⋯ + a2 (to 2n terms) 2a2 = 8n ⇒ a2 = 4 ⇒ a = ± 2 ∴ |a| = |± 2| = 2 |
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