Question

find out quartile deviation and coefficient of quartile deviation from the following data :
Class Interval
0-10
10-20
20-30
30-40
40-50
50-60
Frequency
4
8
5
4
9
10​

Answer 1

N = 40

$\mathtt{Quartile\: deviation}$

$\boxed{\mathtt{qd = \frac{q3 - q1}{2} }}$

$\huge\mathtt{: ⟹ \:Q1}$

$: ⟹ \: size \: of \: \frac{n}{4} th \: term$

$:⟹( \frac{40}{4} )th \: term \: = 10th \: term$

$\mathtt{:⟹\: 10th \: term \: lies \: in \: group\: 10\: - \: 20}$

$\boxed{q1 = l1 + \frac{ \frac{n}{4} - c.f}{f} \times i }$

Here

L1 = Lower limit of class interval

CF = cumulative frequency of the class preceding the first quartile class.

F = frequency of quartile class.

i = class interval.

$: ⟹\: q1 = 10 + ( \frac{10 - 4}{8} ).10$

$: ⟹10 + \frac{60}{8}$

$\boxed{ : ⟹ \: 10 + 7.5 = 17.5 }$

$q3 = size \: of \: 3( \frac{n}{4} )th \: term$

$q3 = \: 10 \times 3 = 30th \: term$

$30th \: term \: falls \: in \: 40 - 50 \: group$

$q3 = l1 + \frac{3 \frac{n}{4} - cf}{f} .i$

L1 = 40

CF = 21

F = 9

i = 10

$: ⟹ \: 40 + \frac{30 - 21}{9} .10$

$: ⟹ \boxed {q3 = 50}$

$\boxed{ \huge{quartile \: deviai tion}}$

$: ⟹ \: \frac{50 + 17.5}{2} = 33.75$

$\huge{ \boxed{33.75}}$

$\boxed{ \huge{coefficient }}$

$: ⟹ \frac{q3 - q1}{q3 + q1}$

$: ⟹ \: \frac{50 - 17.5}{50 + 17.5}$

$: ⟹ \frac{32.5}{67.5}$

$\huge{ \boxed{2.07}}$