A certain data set has the following quartile values

Q1 = 19

Q2 = 30

Q3 = 45

Calculate the Quartile Deviation for this data set

Q1 = 19

Q2 = 30

Q3 = 45

Calculate the Quartile Deviation for this data set

Q1 = 19

Q2 = 30

Q3 = 45

Calculate the Quartile Deviation for this data set

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})

Q.D = (Q

Where Q

Coefficient of quartile deviation= (Q

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

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

Q1=n/4

Q2=2n/4

Q3= 3n/4 ... And so on

Q2=2n/4

Q3= 3n/4 ... And so on

8 9 11 15 16 16 18 20

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