Question

Which of the following is not a measure of dispersion:
$\left( a \right){\text{ }}Quartile$
$\left( b \right){\text{ }}Range$
$\left( c \right){\text{ }}Mean{\text{ }}deviation$
$\left( d \right){\text{ }}Standard{\text{ }}deviation$

Answer 1

As we know that the measure of dispersion is the extent where the distribution is extended or stretched, Range, interquartile range, and standard deviation are the three commonly used measures of dispersion. With the help of this, we can answer this question.

Complete step by step solution:
The proportions of focal inclination are not satisfactory to portray data. Two informational indexes can have a similar mean yet they can be extraordinary. In this way to portray information, one has to know the degree of fluctuation. This is given by the measure of dispersion. Interquartile reach, and standard deviation, and also the range are the three normally utilized measures of dispersion.
The measure of dispersion depends upon the algebraic measures and graphical measures. Where the algebraic measure is further classified into Absolute measures and relative measures. Absolute measures include Range, quartile deviation, mean deviation, and standard deviation. Relative measures include coefficients of range, quartile deviation, variation, and mean deviation.

Hence, Quartile is not the measure of dispersion. A quartile is a measure of the spread of values above or below the mean by dividing the distribution into four groups.
Therefore, the option $\left( a \right)$ is correct.

Note:
For solving this type of question we should have to know the terms available in the options. SD is utilized as a proportion of scattering when mean is utilized as a proportion of focal propensity (i.e., for symmetric mathematical information). And for ordinal information or skewed mathematical information, median and interquartile range are utilized. These are important points we should know that will help to solve such problems.