Question

The standard deviation is expressed in absolute terms (i.e. in the same unit of measure as the data: lbs;inches;dollars;etc) while the coefficient of variation is relative measure?

a. True.
b. False.

Answer 1

a) True

Explanation:

The given statement is true.

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

The standard deviation express the variation of data from the mean and therefore, have the same unit as the data like lbs, inches, dollars, etc.

Coefficient of variation on the other hand is the ratio of standard deviation and mean. It is also a measure of dispersion but since it is a ratio, the units cancel each other.

`C.V = \frac{s}{\bar{x}}`

Thus, coefficient of variation is dimensionless.

Thus, it is a relative measure.