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Question
Find the mean of the following data using assumed mean method:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 8 | 7 | 10 | 13 | 12 |
Solution
Let us first construct the table for di × fi,
where di = xi – A (Assumed mean), as shown below:
| Class | Class Marks `("x"_"i")` |
Frequency `("f"_"i")` |
`"d"_"i" = "x"_"i" - "A"` | `"d"_"i" xx "f"_"i"` |
| 0 – 5 | 2.5 | 8 | – 10 | – 80 |
| 5 – 10 | 7.5 | 7 | – 5 | – 35 |
| 10 – 15 | 12.5 = A | 10 | 0 | 0 |
| 15 – 20 | 17.5 | 13 | 5 | 65 |
| 20 – 25 | 22.5 | 12 | 10 | 120 |
| `sum"f"_"i" = 50` | `sum"f"_"i" "d"_"i" = 70` |
Let A = 12.5,
Then `sum"f"_"i" "d"_"i"` = 70
Now, the required mean
`(bar"x") = "A" + (sum"f"_"i" "d"_"i")/(sum"f"_"i")`
= `12.5 + 70/50`
= 12.5 + 1.4
= 13.9
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