The numerical value of the variance a. is negative if the mean is negative. b. is always larger than the numerical value of the standard deviation. c. is always smaller than the numerical value of the standard deviation. d. can be larger or smaller than the numerical value of the standard deviation.

Step-by-step explanation:

Variance is the sum of squares of all items x from mean.  i.e

Variance =

Being the sum of squares variance can never be negative irrespective of mean being negative.

Std deviation is the square root of variances.  This will thus be less than variance if variance >1 other wise std deviation will be bigger than variance.

Hence option d is right.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: