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 divides 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 quartiles respectively.

If N be the number of observations of the given data. So after arranging them in the ascending or descending order the quartiles are given by:

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

Where, L= lower limit of the quartile class

f = frequency of the quartile class

cf = cumulative frequency of preceding class

i = height of class-interval

The difference between the third and the first quartile is called inter quartile range.

i.e. Inter Quartile Range = Q₃ – Q₁

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

As the units of quartile deviations is same as that of the given observation, the two distribution with different units can not be compared by quartile deviation. To faciliate the comparision of the quartiles of two or more than two series, a relative measure, the coefficient of quartile deviation is used where,

Workout Examples

Example 1: Calculate the quartile deviation and its coefficient of the following data:

24, 32, 46, 48, 39, 42, 28, 25, 26, 24, 38

Solution: Here,

Arranging the data in ascending order,

24, 24, 25, 26, 28, 32, 38, 39, 42, 46, 48

No. of data (N) = 11

Hence, quartile deviation = 8.5 and its coefficient = 0.25.

Example 2: Calculate the quartile deviation and its coefficient from the following data:

*Ages*	12	13	14	15	16	17	18
*No. of Students*	12	21	15	20	17	10	5

Solution: Here,

*Ages (in years)*	*No. of Students (f)*	*Cumulative frequency (cf)*
12 13 14 15 16 17 18	12 21 15 20 17 10 5	12 33 48 68 85 95 *100*
	*N = 100*

Here, N = 100

Hence, quartile deviation = 1.5 and its coefficient = 0.103.

Example 3: Calculate the quartile deviation and its coefficient from the following data:

*Marks*	*0-20*	*20-40*	*40-60*	*60-80*	*80-100*
*No. of Students*	12	20	25	18	5

Solution: Here,

*Marks*	*No. of Students (f)*	*Cumulative frequency (cf)*
*0-20* *20-40* *40-60* *60-80* *80-100*	12 20 25 18 5	12 32 57 75 80
	*N = 80*