The inter-quartile range is a measure of dispersion and is equal to the difference between the third and first quartiles. Half of the inter-quartile range is called semi inter-quartile range or Quartile deviation. Symbolically it is defined as;

Q.D = (Q_{3} - Q_{1})/ 2

Where Q_{1} and Q_{3} are the first and third quartiles of the data. The quartile deviation has an attractive feature that the range "median + Q.D" contains approximately 50 % of the data. The quartile deviation is also an absolute measure of dispersion. Its relative measure is called coefficient of quartile deviation or semi inter-quartile range. It is defined by the relation;

Coefficient of quartile deviation= (Q_{3} - Q_{1})/(Q_{3} + Q_{1})

The following set of data represents the distribution of annual earnings of a random sample of 100 authors: Earnings (£) Authors 1,00 0 but under 1,000 14 1,000 but under 5,000 18 5,000 but under 10,000 14 10,000 but under 20,000 20 20,000 but under 50,000 24 50,000 but under 100,000 7 100,000 but under 150,000 3 (b) Find the lower and upper quartiles and the quartile deviation