Quartile Deviation

Quartiles

For the quartile deviation, let us have an idea about the quartiles. We know that the median divides the given observations arranged in ascending or descending order into two equal parts. Similarly, the quartiles divide the given observations into four equal parts after arranging them in ascending or descending order. So there are three quartiles denoted by Q₁, Q₂ and Q₃ known as the first, the second and the third quartile respectively.

If N be the number of observations of discrete data arranged in the ascending or descending order, then the quartiles are given by the following formula:

In the case of continuous frequency distribution, the quartiles are calculated by the following formula:

Inter Quartiles Range

Inter Quartile Range: The difference between the third and the first quartile is called inter quartile range.

i.e.    Inter Quartile Range = Q₃ – Q₁

 

Quartiles Deviations

The average of deviation of the first quartile and the third quartile taken from median (M) is called the quartile deviation or semi-inter quartile range.

Coefficient of Quartiles

As the unit of quartile deviation is same as that of the given observations, the two distributions with different units cannot be compared by quartile deviation. To facilitate the comparison of the quartiles of two or more than two series, a relative measure, the coefficient of quartile deviation is used, which is calculated as,

Worked Out Examples

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