Calculate upper and lower quartile from the following data:

Variable 0−10 10−20 20−30 30−40 40−50 50−60 60−70

Frequency 10 20 35 40 25 25 15

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Solution

Class Interval Frequency
(f) Cumulative Frequency (c.f.)

0 − 10
10 − 20 10
20 10
30

20 − 30 35 65 Q₁

30 − 40 40 105

40 − 50 25 130 Q₃

50 − 60
60 − 70 25
15 155
170

N=170

$Q_{1} = Size of {(\frac{N}{4})}^{th} item = {(\frac{170}{4})}^{th} = 42 . 5^{th} item$
This lies in the class interval (20-30).

Now,
$Q_{1} = l_{1} = \frac{\frac{N}{4} - c . f .}{f} \times i or, Q_{1} = 20 + \frac{42.5 - 30}{35} \times 10 \Rightarrow Q_{1} = 23.57 Thus, the value of lower quartile is 23.57 . Q_{3} = Size of 3 {(\frac{170}{4})}^{th} = 127 . 5^{th} item This lies in the class interval (40 - 50) . Q_{3} = l_{1} = \frac{3 (\frac{N}{4}) - c . f .}{f} \times i or, Q_{3} = 40 + \frac{127.5 - 105}{25} \times 10 \Rightarrow Q_{3} = 49 Thus, the value of upper quartile is 49 .$

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

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

Variables	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	?	40	?	25	15

Valuable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	7	12	18	25	16	14	8

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

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	2	18	30	45	35	20	6	3