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  • If each observation of the data is increased by 5, then their mean (A) remains the same (B) becomes 5 times the original mean (C) is decreased by 5 (D) is increased by 5

If each observation of the data is increased by 5, then their mean

(A) remains the same

(B) becomes 5 times the original mean

(C) is decreased by 5

(D) is increased by 5

Answers (2)

Answer : D

Let x_{1},x_{2}......x_{n} be the n observations.

\Rightarrow old mean

\bar{x}_{old}=\frac{\sum_{i=1}^{n}x_{i}}{n} \; \; \; \; \; \; \; \; \; ..(i)

Now adding 5 to each observation, the new mean becomes.

\bar{x}_{new}=\frac{\left ( x_{1}+5 \right )+\left ( x_{2}+5 \right )+....+\left ( x_{n}+5 \right )}{n}

\bar{x}_{new}=\frac{\left ( x_{1}+x_{2}+.....+x_{n} \right )+\left ( 5+5+5..... \right ) \text {n times}}{n}

\bar{x}_{new}=\frac{\left ( x_{1}+x_{2}+.....+x_{n} \right )+5n}{n}

\bar{x}_{new}=\frac{\sum_{i=1}^{n}x_{i}}{n}+5=\bar{x}_{old}+5                           (from eq. (i))

\bar{x}_{new}=\bar{x}_{old}+5

Hence, the new mean is increased by 5.

Therefore option (D) is correct.

Posted by

infoexpert23

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D.is
Posted by

Hammad Ansari

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