Which of the following pertaining to the standard deviation of a distribution ca

Question

Which of the following pertaining to the standard deviation of a distribution can be assumed false?

A. If a distribution has a mean of 10 and a standard deviation of 2, we can assume that at least 75% of the data falls within the following bound (6, 14)

B. The standard deviation is mathematically equivalent to the square root of the average of the sum of squares in a distribution.

C. The standard deviation is unit-less, and thus is frequently a better option for describing the distribution of a dataset.

D. A distribution containing the following points (3, 5, 7, 9) will report a drastically different standard deviation were an observation of 21 to be added.

Please explain your answer choice too. Thank you.

Explanation / Answer

C. The standard deviation is unit-less, and thus is frequently a better option for describing the distribution of a dataset.

The above statement is False

Standard deviation is having same unit as that of the mean. So, the statement give above is wrong

P.S- in statement B, an error is there. It should be ".....sum of squares of deviation from mean in a distribution." I believe it is a typing error. Statement C is definitely wrong. If multiple options can be marked as wrong, you can mark statement B as well, because of the above mentioned reason.

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