NDA 2022 Maths · Mathematics · Statistics · medium

Adding a constant to every observation leaves the standard deviation unchanged. 2. Multiplying every observation by c multiplies the standard…

Single correct option

Which of the following statements is/are correct?
1. Adding a constant to every observation leaves the standard deviation unchanged.
2. Multiplying every observation by

c

multiplies the standard deviation by

|c|

A. $1$ only
B. $2$ only
C. Both $1$ and $2$
D. Neither $1$ nor $2$

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Answer: (C) Both $1$ and $2$

Spread is unaffected by shifting, so Statement 1 holds. Scaling by

c

scales deviations by

c

, hence

\sigma\to|c|\sigma

, so Statement 2 also holds. Both are correct; note the absolute value if

c<0

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