# Quartile Deviation and its Coefficient

__Quartile Deviation__

Quartile deviation is based on the lower quartile and the upper quartile . The difference is called the inter quartile range. The difference divided by is called semi-inter-quartile range or the quartile deviation. Thus

The quartile deviation is a slightly better measure of absolute dispersion than the range, but it ignores the observations on the tails. If we take difference samples from a population and calculate their quartile deviations, their values are quite likely to be sufficiently different. This is called sampling fluctuation, and it is not a popular measure of dispersion. The quartile deviation calculated from the sample data does not help us to draw any conclusion (inference) about the quartile deviation in the population.

__Coefficient of Quartile Deviation__

A relative measure of dispersion based on the quartile deviation is called the coefficient of quartile deviation. It is defined as:

Coefficient of Quartile Deviation

It is a pure number free of any units of measurement. It can be used for comparing the dispersion of two or more sets of data.

__Example__

The wheat production (in Kg) of 20 acres is given as: 1120, 1240, 1320, 1040, 1080, 1200, 1440, 1360, 1680, 1730, 1785, 1342, 1960, 1880, 1755, 1720, 1600, 1470, 1750, and 1885. Find the quartile deviation and coefficient of quartile deviation.

__Solution__:

After arranging the observations in ascending order, we get

1040, 1080, 1120, 1200, 1240, 1320, 1342, 1360, 1440, 1470, 1600, 1680, 1720, 1730, 1750, 1755, 1785, 1880, 1885, 1960.

__Example__:

Calculate the quartile deviation and coefficient of quartile deviation from the data given below:

Maximum Load(short-tons) |
Number of Cables |

__Solution__:

The necessary calculations are given below:

Maximum Load(short-tons) |
Number of Cables() |
ClassBoundaries |
CumulativeFrequencies |

lies in the class

Where , , , and

lies in the class

Where , , , and