Question

Evaluate lower quartile and upper quartile from the following series.

Variable	5	10	15	20	25	30	35	40
Frequency	16	18	22	21	24	14	11	9

Answer 1

Variable	Frequency(f)	Cumulative Frequency(c .f.)
5	16	16
10	18	34
15	22	56
20	21	77
25	24	101
30	14	115
35	11	126
40	9	135
	N = 135

Q₁ = size of \((\frac{N+1}4)^{th}\) item

Or, Q₁ = size of \((\frac{135+1}{4})^{th}\) item

= Q₁ = 34^th item

Upper Quartile

Q₁ = size of 3 \((\frac{N+1}{4})^{th}\) item

or, Q₁ = size of 3 \((\frac{135+1}{4})^{th}\) item

= Q₁ = 102^nd item

This corresponds to 115 in the cumulative frequency. Hence, upper quartile is 30.