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Question

The mean of four observations is 3. If the sum of the squares of the observations is 48, then their standard deviation is


A

7

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B

2

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C

3

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D

5

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Solution

The correct option is C

3


Explanation for the correct option:

Find the standard deviation for the given observations.

It is given that, the mean of four observations is 3 and the sum of the squares of the observations is 48.

We know that, the standard deviation σ is given by σ=i=1n(xi2)n-x¯2.

So, the standard deviation σ for the given observation is as follows:

σ=484-32σ=12-9σ=3

Therefore, the standard deviation σ for the given observation is 3.

Hence, option C is the correct option.


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