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Question
Find the mean of the following frequency distribution is 57.6 and the total number of observation is 50.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
| Frequency | 7 | `f_1` | 12 | `f_2` | 8 | 5 |
Solution
| Class | Frequency `(f_i)` | Mid values`(x_i)` | `(f_i xx x_i)` |
| 0-20 | 7 | 10 | 70 |
| 20-40 | `f_1` | 30 | 30`f_1` |
| 40-60 | 12 | 50 | 600 |
| 60-80 | 18-`f_1` | 70 | 1260-70`f_1` |
| 80-100 | 8 | 90 | 720 |
| 100-120 | 5 | 110 | 550 |
| Total | `sum f_i = 50` | `sum (f_i xx x_i ) = 3200-40f_1` |
We have:
`7 + f_1 + 12 + f_2 + 8 + 5 = 50`
`⇒ f_1 + f_2 = 18`
`⇒ f_2 = 18 – f_1`
∴ Mean, x =`(Σ_i (f_ixx x_i))/(Σi f_i)`
⇒ 57.6 =`(3200 − 40f_1)/50`
`⇒ 40f_1 = 320`
`∴ f_1 = 8`
`And f_2 = 18 – 8`
`⇒ f_2 = 10`
∴ The missing frequencies are` f_1 = 8 and f_2 = 10.`
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