Question

Find Q₁, Q₃, D₈ and P₆₇ of the following data:

Size of Shares	4	4.5	5	5.5	6	6.5	7	7.5	8
Frequency	10	18	22	25	40	15	10	8	7

Answer 1

Size of Shares	Frequency	Cumulative Frequency
4	10	10
4.5	18	28
5	22	50
5.5	25	75
6	40	115
6.5	15	130
7	10	140
7.5	8	148
8	7	155
	N = 155

Q₁ = Size of `(("N" + 1)/4)^"th"` value

= Size of `((155 + 1)/4)^"th"` value

= Size of 39^th value

Q₁ = 5

Q₃ = Size of `[3(("N" + 1)/4)]^"th"` value

= Size of `(3 xx 156/4)^"th"` value

= Size of 117^th value

Q₃ = 6.5

D₈ = Size of `[8(("N" + 1)/10)]^"th"` value

= Size of `[8((155 + 1)/10)]^"th"` value

= Size of `(8 xx 156/10)^"th"` value

= Size of 124.8^th value

D₈ = 6.5

P₆₇ = Size of `[67(("N" + 1)/100)]^"th"` value

= Size of `((67 xx 156)/100)^"th"` value

= Size of 104.52^th value

P₆₇ = 6