# Find the missing frequency given that the median of distribution is 1504. Life in hours 950 – 1150 1150 –1350 1350 – 1550 1550 – 1750 1750 – 1950 1950 – 2150 No. of bulbs 20 43 100 – 23 13 - Mathematics and Statistics

Sum

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

#### Solution

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

Concept: Concept of Median
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