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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Statistics

NDA 2015 · Mathematics · Statistics

The mean and the variance 10 observations are given to be 4 and 2...

The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2 , the mean and the variance of the new series will be respectively

Options

  1. A8 and 20
  2. B8 and 4
  3. C8 and 8
  4. D80 and 40

Correct answer

C. 8 and 8

Step-by-step solution

Mean (X‾)=4(\overline{\mathrm{X}})=4 Variance (X)=2(\mathrm{X})=2 Number of observations =10=10 New average =(4×10)×210=8=\frac{(4 \times 10) \times 2}{10}=8 New variance =(2)2×=(2)^2 \times Variance (X)=4×2=8∴(X)=4 \times 2=8\therefore \quad Option (C) is correct.
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