Question

 Find the missing frequency given that the median of the distribution is 1504.

Life in hours	950 – 1150	1150 – 350	1350 – 1550	1550 – 1750	1750 – 1950	1950 – 2150
No. of bulbs	20	43	100	–	23	13

Answer 1

Let x be the missing frequency of the class 1550 – 750.

Life in hours	No. of bulbs (f)	Less than Cumulative frequency (c.f.)
950 – 1150	20	20
1150 – 1350	43	63
1350 – 1550	100	163
1550 – 1750	x	163 + x
1750 – 1950	23	186 + x
1950 – 2150	13	199 + x
Total	199 + x

Here, N = 199 + x
Given, Median (Q₂) = 1504
∴ Q₂ lies in the class 1350 – 1550
∴ L = 1350, f = 100, c.f. = 63, h = 200,

 `"2N"/(4)=(199+"x")/(2)`

Q₂= `"L"+"h"/"f"(("2N")/4 - "c.f.")`

1540 = `1350 + (200)/(100)((199 + "x")/2 - 63)`

1540 – 1350 = `2((199 + "x"-126)/2)`

∴ 154  = 199 + x – 126
∴ 154 = 73 + x
∴ x = 81