Question

Which of the following is not the measure of dispersion?
A. Quartile dispersion
B. Range
C. Mean deviation
D. None of these.

Answer 1

Hint:
Quartile dispersion is the measure of the central tendency and the 2nd quartile is equal to median. Also range and mean deviation are the measure of the dispersion.

Complete step by step solution:
We need to find which of the following is not the measure of dispersion? So in statistics the dispersion is the extent up to which the distribution can be squeezed. Common examples of the dispersion are the standard deviation, variance, interquartile range. The measure of the statistical dispersion is the non-negative real number that is zero. If all the data are the same and increases as the data becomes more dispersed. So here we are given the quartile dispersion, range, mean deviation and we need to find which is the measure of the dispersion and e=which one is not.
So when we talk about range then we can say that it is the simplest form of the dispersion. It is the difference between the two extreme observations of the data. If $a,b$ are the two extreme values then we can say that ${\text{Range}} = b - a$
When we talk about the quartile dispersion then we can say that it divides the data sets into the quarters. The first quartile is the middle number between the smallest number and the median of the data. The second one represents the median. The third is the middle number between the median and the largest number.so quartile deviation is $Q = \dfrac{1}{2}({Q_3} - {Q_1})$
Mean deviation is the arithmetic means of the absolute deviation of the observations from a measure of central tendency and it is given by
Mean deviation$ = \dfrac{1}{n}\sum\limits_{i = 1}^n {\left| {{x_i} - x} \right|} $
So here we saw that all the three are measures of the dispersion.

Hence D is the correct answer.

Note:
Standard deviation, variance, enthalpy these are also the measure of the deviations and the demerit of range is that it is based on the two extreme values and get affected by some fluctuations and all the drawbacks of range are overcome by the quartile deviation.