Coefficient Of Dispersion is used to compare the variability of the two data set that differ widely in their averages, or have been measured in different units.

Coefficient Of Dispersion, based upon standard deviation, is given by:

$C.D=\frac{\sigma}{\stackrel{\u2015}{x}}$

where $\sigma$ is standard deviation and $\stackrel{\u2015}{x}$ is mean of the data set.

Coefficient Of Variation is defined as 100 times the coefficient of dispersion based upon standard deviation, i.e.,

$C.V=100\times \left(\frac{\sigma}{\stackrel{\u2015}{x}}\right)$.

The data set that has lesser C.V is said to be more consistent than the other data set.

There are four types of scales for measurement, i.e.,

a. Ratio scale: data is continuous and have a defined and meaningful zero.

b. Interval scale: data lie within a defined interval and have no defined true zero.

c. Nominal scale: have various categories with no specific order.

d. Ordinal scale: have various categories with a specific order.

Now, for the given question,

(a.) Since Coefficient Of Variation is used for the data measured on a ratio scale, i.e., the data should be continuous and have a defined and meaningful zero. It is not used for the other scales like nominal, ordinal and interval scale. Therefore, option (a.) is incorrect.

(b.) Since Coefficient Of Dispersion are pure numbers independent of units of measurement, it implies that Coefficient Of Variation is also a pure number, independent of the units of measurement that are used to compare the two numeric data sets. Therefore, option (b.) is correct.

(c.) Since Coefficient Of Variation is used for the data measured on a ratio scale, i.e., the data should be continuous and have a defined and meaningful zero, and not for the other scale, option (c.) is incorrect.

(d.) Since for grouped data, we can calculate the mean and standard deviation, and hence, are able to calculate and compare the Coefficient Of Variation for two data set, option (d.) is correct.

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