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Question
The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:
| Marks(x) | 15 | 20 | 22 | 24 | 25 | 30 | 33 | 38 | 45 |
| Frequency (f) | 5 | 8 | 11 | 20 | 23 | 18 | 13 | 3 | 1 |
Find the average number of marks.
Solution
Let the assumed mean (A) = 25
| Marks (x1) | Frequency (f1) |
u1= x1 - A x1 - 25 |
f1u1 |
| 15 | 5 | -10 | -50 |
| 20 | 8 | -5 | -40 |
| 22 | 11 | -3 | -33 |
| 24 | 20 | -1 | -20 |
| 25 | 23 | 0 | 0 |
| 30 | 18 | 5 | 90 |
| 33 | 13 | 8 | 104 |
| 38 | 3 | 13 | 39 |
| 45 | 1 | 20 | 20 |
| N = 102 | `sumf_1"u"_1=110` |
Average number of marks `=A + (sumf_1"u"_1)/N`
`=25+110/102`
`=(2550+110)/102`
`=2660/102`
= 26.08(Approx)
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