Question

Find out Q₃ from the given data.

(Use the population figures as numerical data)

Year	Population (in Crores)
1951	36.1
1961	43.9
1971	54.8
1981	68.3
1991	84.6
2001	102.7
2011	121.02

Answer 1

Year	Population (in Crores)	Cumulative frequency (cf)
1951	36.1	36.1
1961	43.9	80
1971	54.8	134.8
1981	68.3	203.1
1991	84.6	287.7
2001	102.7	390.4
2011	121.02	511.42
	N = 511.42

Q₃ = size of 3`((n+1)/4) ^"th observation"`

Q₃ = size of 3`((511.42+1)/4) ^"th observation"`

Q₃ = size of 3`((512.42)/4) ^"th observation"`

Q₃ = size of 3 (128.105)^th observation

Q₃ = size of 384.315^th observation

The size of 384.315^th observation lies in cf 390.4

Hence quartile value in the year 2001.

Q₃ = the year 2001.