Compute quartile deviation for each of the following tables.
Class interval frequency
$1 - 9$ $4$
$10 - 19$ $3$
$20 - 29$ $20$
$30 - 39$ $12$
$40 - 49$ $5$
$50 - 59$ $8$
$60 - 69$ $14$
$70 - 79$ $27$
$80 - 89$ $2$
$90 - 99$ $5$

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Solution

Class Interval

Frequency

Cumulative Frequency

1-9

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

4

3

20

12

5

8

14

27

2

5

4

7

27

39

44

52

66

93

95

100

$N_{1}$ for $Q_{1} = \frac{100}{4} = 25$

$Q_{1} = L + \frac{N - C_{f}}{f} \times i \Rightarrow Q_{1} = 20 + \frac{25 - 27}{20} \times 10 \Rightarrow Q_{1} = 0.5 + 20 - 1 = 18.5$

$N_{3}$ for $Q_{3} = \frac{3 N}{4} = 75$
$\Rightarrow Q_{3} = 69.5 + \frac{75 - 93}{70} \times 10 \Rightarrow Q_{3} = 66.92$

Therefore, $\frac{Q_{3} - Q_{1}}{2} = \frac{66.92 - 18.5}{2} = 24.21.$

Suggest Corrections

Marks	10−19	20−29	30−39	40−49	50−59	60−69	70−79	80−89	90−99
Number of Students	29	87	181	247	263	133	40	9	2

X	:	30-40	40-50	50-60	60-70	70-80	80-90	90-100
f	:	6	10	16	14	10	5	2

$C . I .$	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$
$f$	$8$	$16$	$17$	$34$	$10$	$5$	$10$

$C I$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 90$
$f$	$3$	$7$	$5$	$11$	$6$	$8$	$4$	$5$