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Question
In the following table, Σf = 200 and mean = 73. Find the missing frequencies f1, and f2.
| x | 0 | 50 | 100 | 150 | 200 | 250 |
| f | 46 | f1 | f2 | 25 | 10 | 5 |
Solution
We have,
| x | f | fx |
| 0 | 46 | 0 |
| 50 | f1 | 50f1 |
| 100 | f2 | 100f2 |
| 150 | 25 | 3750 |
| 200 | 10 | 2000 |
| 250 | 5 | 1250 |
| Σf = 86 + f1 + f2 | Σfx = 7000 + 50f1 + 100f2 |
Given, Σf = 200
`=>` 86 + f1 + f2 = 200
`=>` f1 + f2 = 114 ...(i)
Mean = `(Σfx)/(Σf)`
`=> 73 = (7000 + 50f_1 + 100f_2)/200`
`=>` 7000 + 50f1 + 100f2 = 14600
`=>` 50f1 + 100f2 = 7600
`=>` f1 + 2f2 = 152 ...(ii)
Subtracting (ii) from (i), we get
f2 = 38
`=>` f1 = 114 – 38 = 76
Hence, f1 = 76 and f2 = 38
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