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:

C. 0.5

Step-by-step 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.  

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

where, [tex]\bar{x}[/tex] is mean of the distribution.

And, Variance is the square of the Standard deviation.