Question

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

A. 2.5
B. 1.75
C 0.5
D 1.25

Answer 1

Hello.

The answer is

C.0.5

the standard is .50 and all of the other options are larger so it would be c.

Have a nice day

Answer 2

C. 0.5

Explanation:

We know that the relation between Standard Deviation and Variance is given by,

Standard Deviation = √(Variance)

Thus,

A. When Variance = 2.5,⇒ Standard Deviation = 1.58

B. When Variance = 1.75,⇒ Standard Deviation = 1.32

C. When Variance = 0.5,⇒ Standard Deviation = 0.71

D. When Variance = 1.25,⇒ Standard Deviation = 1.12

Hence Variance which has greater Standard deviation is Option C.

Further,

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

`Standard deviation(\sigma) = \sqrt{(1)/(n)\sum_(i=1)^(n){(x_(i)-\bar{x})^(2)} }`

where,
`\bar{x}` is mean of the distribution.

And, Variance is the square of the Standard deviation.