Question

If a data point has a corresponding z-score of -1.5, then it is one and a half standard deviations above the mean value. 1. True 2. False

Answer 1

Answer: False.

Step-by-step explanation:

For any random variable x,

Formula to calculate the z-score : $z=\dfrac{x-\mu}{\sigma}$

, where $\mu$ = Mean

$\sigma$ = Standard deviation

Let x be the data point has a corresponding z-score of -1.5.

Then , we have

$-1.5=\dfrac{x-\mu}{\sigma}$

$-1.5\sigma=x-\mu$

$\mu-1.5\sigma=x$

i.e. x is one and a half standard deviations below the mean value.

( one and a half =$1+\dfrac{1}{2}=1.5$ )

Therefore , the given statement is false.