Quartile Deviation
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 case of continuous frequency distribution, the quartiles are calculated by the following formula:
Inter Quartile Range: The difference between the
third and the first quartile is called inter
quartile range.
i.e. Inter Quartile Range = Q3 – Q1
Quartile Deviation: 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 Quartile Deviation: 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,
Workout Examples
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