GATE CS 2012 Q.64 (GA Q.64): Quantitative Aptitude

Which of the following assertions are CORRECT?

$P$ : Adding 7 to each entry in a list adds 7 to the mean of the list
$Q$ : Adding 7 to each entry in a list adds 7 to the standard deviation of the list
$R$ : Doubling each entry in a list doubles the mean of the list
$S$ : Doubling each entry in a list leaves the standard deviation of the list unchanged

$P, Q$

$Q, R$

$P, R$

$R, S$

Official answer and solution

Official answer: C
From: Official GATE 2012 answer key

Solution

Evaluate the effects of linear transformations on the mean and standard deviation of a dataset.

For a dataset with mean $\mu$ and standard deviation $\sigma$ :
Adding a constant $c = 7$ :

New mean $\mu' = \mu + 7$ . (Assertion $P$ is CORRECT).
New standard deviation $\sigma' = \sigma$ . The spread is unaffected by a uniform shift. (Assertion $Q$ is INCORRECT).

Multiplying by a constant $k = 2$ :

New mean $\mu'' = 2\mu$ . (Assertion $R$ is CORRECT).
New standard deviation $\sigma'' = 2\sigma$ . Multiplying doubles the dispersion. (Assertion $S$ is INCORRECT).

Therefore, assertions $P$ and $R$ are CORRECT, matching option (C).

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2012 Computer Science and Information Technology (CS)
Question: 64 of 65, printed as GA Q.64
Section: General Aptitude

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