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
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