# How Do I Calculate Quartile Deviation?

A certain data set has the following quartile values

Q1 = 19
Q2 = 30
Q3 = 45

Calculate the Quartile Deviation for this data set
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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 = (Q3 - Q1)/ 2

Where Q1 and Q3 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= (Q3 - Q1)/(Q3 + Q1)
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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
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Q1=n/4
Q2=2n/4
Q3= 3n/4 ... And so on
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