Quartile Deviation for Ungrouped Data

 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 ungrouped data.


Ungrouped Data


Problem: Following are the runs scored by a batsman in last 20 test matches: 96, 70, 100, 96, 81, 84, 90, 89, 63, 90, 34, 75, 39, 82, 85, 86, 76, 64, 67, and 88. Calculate the Quartile Deviation and Coefficient of Quartile Deviation.


Arrange data in ascending order:


34, 39, 63, 64, 67, 70, 75, 76, 81, 82, 84, 85, 86, 88, 89, 90, 90, 96, 96, 100


First Quartile (Q1)


The calculation of First quartile is shown in the figure given below.



Third Quartile (Q3)


The formula for the calculation of third quartile is given as:



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



Also see calculation of Quartile Deviation for grouped data

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20 responses to Quartile Deviation for Ungrouped Data

@ Erick:

Quartile deviation= .5 * Inter quartile range

Semi quartile range is also the same……So basically

QD = Semi quartile range

Really it helped but i have a question…
take example from above data
Q1 = 5.25th observation
if it was
Q1 = 5th observation
then we will simply take the 5th observation that is 67.
Am i right?

Well i have worked out the question but for the coefficient of quartile deviation its 22 divide by 157.5, my final answer is 0.1397. please confirm me the right answer.

thanking you beforehand

Sorry, My query was on this ungrouped data distriution….how did u get the value of Q1 and Q3(by what formula) if u could pls explain……

answer of coefficient of quartile deviation is wrong. in last formula there is 22 instead of 11. and the correct answer is 0.139

Am sorry but I think that this whole formula is wrong from the start. The data is even not old so the is no way you can use the formula you have used. n=20, and 20 is an old number. therefore there is no need of adding 1 when looking for Q1 and Q3. somebody prove me write or wrong.

Q1=5, and Q3=15.

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