Question

A sample with which of these variances has a standard deviation that is greater than the variance?

A. 2.25
B. 1.75
C. 0.75
D. 1.25

Answer 1

Standard deviation is the square root of the variance. For the square root of a number to be greater than the number, the number must be between 0 and 1.
Hence, for the standard variation to be greater than the variance, the variance must be between 0 and 1.

Answer: C [0.75]

Answer 2

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

What is standard deviation?

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value

Here we have to find a sample with standard deviation greater than the variance.

We know that Standard deviation is the square root of the variance so if we want a sample with greater Standard deviation than the variance  then it's variance  should be less than one as we know that if

$0 < x < 1 \Rightarrow \sqrt x > x$

And here given variances are

2.25, 1.75,0.75 and 1.25

Hence 0.75 is correct answer

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

To learn more about standard deviation visit :https://brainly.com/question/12402189