# Quartile Deviation and its Coefficient

__Quartile Deviation__**:**

It 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 observation 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. 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 pure number free of any units of measurement. It can be used for comparing the dispersion in two or more than two 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