Question

Find the value of Q₁ and Q₃ for the following data

X	5	8	12	15	19	24	30
f	4	3	2	4	5	2	4

1. 8 and 12
2. 12 and 8
3. 8 and 30
4. 6 and 24
5.

Answer 1

Correct Answer - Option 3 : 8 and 30

Calculation

x	f	Cf
5	4	4
8	3	7
12	2	9
15	4	13
19	5	18
24	2	20
30	4	24
Total	N = 24

Q₁ = (N + 1)/4^th term

⇒ (24 + 1)/4 = 25/4^th term

⇒ 6.25^th term

∴ 6.25^th lies in cf of 7

∴ The value of Q₁ is 8

Q₃ = 3(N + 1)/4

⇒ Q₃ = 3(24 + 1)/4  18.75^th term

⇒ 18.75^th lies in cf of 20

∴ The value of Q₃ is 30