Maharashtra State BoardHSC Commerce 11th
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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
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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
  Is there an error in this question or solution?
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