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Question
Find the mean from the following frequency distribution of marks at a test in statistics:
| Marks(x) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| No. of students (f) | 15 | 50 | 80 | 76 | 72 | 45 | 39 | 9 | 8 | 6 |
Solution
Let the assumed mean (A) = 25
| Marks (x1) | No. of students (f1) |
u1 = x1 - A = x1 - 25 |
f1u1 |
| 5 | 15 | -20 | -300 |
| 10 | 50 | -15 | -750 |
| 15 | 80 | -10 | -800 |
| 20 | 76 | -5 | -380 |
| 25 | 72 | 0 | 0 |
| 30 | 45 | 5 | 225 |
| 35 | 39 | 10 | 390 |
| 40 | 9 | 15 | 135 |
| 45 | 8 | 20 | 160 |
| 50 | 6 | 25 | 150 |
| N = 400 | `sumf_1"u"_1=-1170` |
Mean `=A+(sumf_1"u"_1)/N`
`=25+(-1170)/400`
`=(10000-1170)/400`
= 22.075
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