Inter Quartile Range

Inter-Quartile Range is defined as the difference between two extreme quartiles of a series,

Thus, absolute IQR = Q₃ – Q₁

And  Coeff.IQR   Q₃ – Q_{1/ Q3 + Q4}

Where, Q3 = Upper quartile of a series

and        Q1 = Lower quartile of a series.

From the formula cited above, it must be clear that the determination of the IQR depends entirely upon the values of the two extreme quartiles i.e., Q3 and Q1.

Merits and Demerits

The relative merits, and demerits of IQR can be pointed out as under:

Merits

• It is rigidly defined.
• It is simple to calculate.

Demerits

• It is not based on all the observation of the series, since first 25%, and last 25% of the series are completely ignored in its calculation.
• It is not capable of further algebraic treatment.
• It does not give any idea of dispersion of the items from the central value of the series.
• It is affected by fluctuations in sampling.

It takes more time to calculate as it involves determination of the two quartiles in the first instance.