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Question
The arithmetic mean of the following frequency distribution is 53. Find the value of k.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 12 | 15 | 32 | k | 13 |
Solution
| Class | Frequency (fi) | xi | di = xi -50 | fidi |
| 0 - 20 | 12 | 10 | -40 | -480 |
| 20 - 40 | 15 | 30 | -20 | -300 |
| 40 - 60 | 32 | 50 | 0 | 0 |
| 60 - 80 | k | 70 | 20 | 20k |
| 80 - 100 | 13 | 90 | 40 | 520 |
| ∑fi = 72 + k | fidi = -260 + 20k |
`bar"x" = "a" + (∑"f"_"i" "d"_"i")/(∑"f"_"i")`
`53 = 50 + ((-260 + 20"k"))/(72 +" k")`
⇒ 3 = `(-260 + 20"k")/(72 +"k")`
⇒ `216 + 3"k" = -260 + 20"k"`
⇒ `476 = 17"k"`
⇒ k = 28
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