Question

Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain.

Answer 1

Answer:

We can define the standard deviation as the square root of the variance.

The unit for standard deviation and mean are same. But the variance is expressed in square units.

The variance cannot be negative, because then, you cannot find the square root of it.

Similarly, under no circumstances, the standard deviation can be negative. The standard deviation formula is calculated by using squares of the numbers, and square of a number cannot be negative.

Answer 2

The relation between variance and standard deviation is,

                      $Deviation=\sqrt{Variance}$

Relationship between variance and standard deviation:

Standard deviation is the spread of a group of numbers from the mean. The variance measures the average degree to which each point differs from the mean.

• The standard deviation is the square root of the variance.

• We can define the standard deviation as the square root of the variance.

                      $Deviation=\sqrt{Variance}$

• The unit for standard deviation and mean are same. But the variance is expressed in square units.

Since, standard deviation as the square root of the variance. Thus, variance can not be negative.

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