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# Inter Quartile Range and Quartile Deviation

It is also called as semi-inter quartile range.

Inter Quartile Range and Quartile Deviation

The quartiles Q1, Q2 and Q3 have been introduced and studied.

Inter quartile range is defined as: Inter quartile Range (IQR) = Q3-Q1

Quartile Deviation is defined as, half of the distance between Q1 and Q3.

Quartile Deviation Q.D = Q3-Q1 / 2 It is also called as semi-inter quartile range.

## Coefficient of Quartile Deviation

The relative measure corresponding to QD is coefficient of QD and is defined as:

Coefficient of Quartile Deviation = Q3-Q1 / Q3+Q1 ## Merits:

·           It is not affected by the extreme (highest and lowest) values in the data set.

·           It is an appropriate measure of variation for a data set summarized in open-ended class intervals.

·           It is a positional measure of variation; therefore it is useful in the cases of erratic or highly skewed distributions.

## Limitations:

·           The QD is based on the middle 50 per cent observed values only and is not based on all the observations in the data set, therefore it cannot be considered as a good measure of variation.

·           It is not suitable for mathematical treatment.

·           It is affected by sampling fluctuations.

·           The QD is a positional measure and has no relationship with any average in the data set.

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11th Statistics : Chapter 6 : Measures of Dispersion : Inter Quartile Range and Quartile Deviation | Merits, Limitations, Solved Example Problems | Statistics