From the following series, calculate lower quartile and upper quartile.

Variable 5 10 15 20 25 30 35 40

Frequency 16 18 22 21 24 14 11 9

Open in App

Solution

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

Lower Quartile

$Q_{1} = Size of {(\frac{N + 1}{4})}^{th} item or, Q_{1} = Size of {(\frac{135 + 1}{4})}^{th} item \Rightarrow Q_{1} = 34^{th} item$
This corresponds to 34 in the cumulative frequency.
Hence, lower quartile is 10.

Upper Quartile

$Q_{3} = Size of 3 {(\frac{N + 1}{4})}^{th} item or, Q_{3} = Size of 3 {(\frac{135 + 1}{4})}^{th} item \Rightarrow Q_{3} = 102^{nd} item$

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

Suggest Corrections

Size	5−10	10−15	15−20	20−25	25−30	30−35	35−40	40−45	45−50
Frequency	6	10	18	30	15	12	10	6	4

Class Interval	1−5	6−10	11−15	16−20	21−25	26−30	31−35
Frequency	2	8	15	35	20	10	14

Class Interval	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	4	8	5	4	9	10

Size	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Variable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	35	40	25	25	15