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प्रश्न
The mean of the following frequency distribution is 25. Find the value of f.
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 5 | 18 | 15 | f | 6 |
उत्तर
Let us first construct a table for xi × fi, as shown below:
| Class | Frequency `("f"_"i")` |
Class Mark `("x"_"i")` |
`"x"_"i" xx "f"_"i"` |
| 0 – 10 | 5 | 5 | 25 |
| 10 – 20 | 18 | 15 | 270 |
| 20 – 30 | 15 | 25 | 375 |
| 30 – 40 | f | 35 | 35 f |
| 40 – 50 | 6 | 45 | 270 |
| Total | `sum"f"_"i" = 44 + "f"` | `sum"x"_"i" "f"_"i" = 940 + 35 "f"` |
Now, Mean `(bar"x") = (sum"x"_"i" "f"_"i")/(sum"f"_"i")`
∴ 25 = `(940 + 35 "f")/(44 + "f")`
⇒ 1100 + 25 f = 940 + 35 f
⇒ 35 f – 25 f = 1100 – 940
⇒ 10 f = 160
⇒ f = `160/10`
⇒ f = 16
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