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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Statistics

NDA 2016 · Mathematics · Statistics

The mean of the series x_1, x_2, , x_n is X . If x_2 is replaced by...

The mean of the series x1,x2,…,xnx_1, x_2, \ldots, x_n is X‾\overline{\mathrm{X}}. If x2\mathrm{x}_2 is replaced by λ\lambda, then what is the new mean?

Options

  1. AX‾−x2+λ\overline{\mathrm{X}}-\mathrm{x}_2+\lambda
  2. BXˉ−x2−λn\frac{\bar{X}-x_2-\lambda}{n}
  3. CXˉ−x2+λn\frac{\bar{X}-\mathrm{x}_2+\lambda}{\mathrm{n}}
  4. DnX‾−x2+λn\frac{\mathrm{n} \overline{\mathrm{X}}-\mathrm{x}_2+\lambda}{\mathrm{n}}

Correct answer

D. nX‾−x2+λn\frac{\mathrm{n} \overline{\mathrm{X}}-\mathrm{x}_2+\lambda}{\mathrm{n}}

Step-by-step solution

Mean of series (x1,x2,x3……xn)\left(x_1, x_2, x_3 \ldots \ldots x_{\mathrm{n}}\right)xˉ=x1+x2+x3+….xnn⇒x1+x2+x3+….xn=nxˉ\begin{aligned} & \bar{x}=\frac{x_1+x_2+x_3+\ldots . x_n}{n} \\ & \Rightarrow x_1+x_2+x_3+\ldots . x_n=n \bar{x} \end{aligned}$NowwewillreplaceNow we will replacex_2byby\lambdasono.ofelementsinserieswillnotchange.Newserieswillincludeso no. of elements in series will not change. New series will include\lambdaandexcludeand excludex_2Hencenewseriessum:Hence new series sum :\left(x_1+x_2+\ldots . . x_n\right)-x_2+\lambda=n \bar{x}+\lambda-x_2NownewmeanNow new mean=\frac{n \bar{x}+\lambda-x_2}{n}=\frac{n \bar{x}-x_2+\lambda}{n}$
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