Question

Let $a$, $b$, $c$, and $d$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a + k, b + k, c + k, d + k$ is:

• A. $kS$
• B. $S + k$
• C. $\frac{S}{k}$
• D. $S$

Answer 1

The Correct Option is D

The standard deviation measures the spread of data points. Adding a constant $k$ to each observation shifts the data uniformly, but it does not affect the spread.

Hence, the standard deviation remains $S$.