Quartile deviation or semi-interquartile range is the dispersion which shows the degree of spread around the middle of a set of data. Since the difference between third and first quartiles is called interquartile range therefore half of interquartile range is called semi-interquartile range also known as quartile deviation. For both grouped and ungrouped data, quartile deviation can be calculated by using the formula:

### Coefficient of Quartile Deviation:

Coefficient of Quartile Deviation is used to compare the variation in two data. Since quartile deviation is not affected by the extreme values therefore it is widely used in the data containing extreme values. Coefficient of Quartile Deviation can be calculated by using the formula:

The concept of quartile deviation and coefficient of quartile deviation can be explained with the help of simple problems for grouped data.

### For Grouped Data

**Problem:** Following are the observations showing the age of 50 employees working in a whole sale center. Find the quartile deviation and coefficient of quartile deviation.

**Solution:**

In case of frequency distribution, quartiles can be calculated by using the formula:

### First Quartile (Q1)

In case of frequency distribution first quartile can be calculated by using the formula given below:

### Third Quartile (Q3)

Like first and second quartile, the third quartile can be calculated by using the formula:

By putting the values into the formulas of quartile deviation and coefficient of quartile deviation we get:

See also calculation of quartile deviation for ungrouped data

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thanks so much. but i have a little bit of correction

in the computation for the third quartile, should it be 60.4375 not 60.63…

but THANKS SO MUCH. i had a hard time understanding this because the formula of my prof is a bit different from yours but when I look at it, they’re just the same. 😀

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Its very easy to understand but if the data is give as…

5_10=3

10_15=5

15_20=7 then how will we find commulative frequecy for such data please iam confused in this i need to know its solution. Thanks

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It was of great help. Thanks so much. Please the correct answer for Q3 is 60.4375.

Thanks. This presentation makes the calculations very simple. Even a high school student can follow through. I now have a good insight on quartile deviation for grouped and ungrouped data.

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It made the understanding of quartiles simple, thanks

The last step I.e while calculating the coefficient of quartile deviation, is faulty…How can 60.63-50.016 =110.60…

Thanks i understand it now

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