Question

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

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

Answer 1

Let x be the missing frequency of the class 1550 – 1750.

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.")`

1504 = `1350 + (200)/(100)((199 + "x")/2 - 63)`

1504 – 1350 = `2((199 + "x"-126)/2)`

∴ 154  = 199 + x – 126

∴ 154 = 73 + x

∴ x = 81