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Question
Find the mean marks per student, using assumed-mean method:
| Marks | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| Number of Students |
12 | 18 | 27 | 20 | 17 | 6 |
Solution
| Class | Frequency `(f_i)` | Mid values `(x_i)` | Deviation `(d_i) d_i = (x_i – 25)` |
`(f_i× d_i)` |
| 0 –10 | 12 | 5 | -20 | -240 |
| 10 –20 | 18 | 15 | -10 | -180 |
| 20 – 30 | 27 | 25 = A | 0 | 0 |
| 30 – 40 | 20 | 35 | 10 | 200 |
| 40 – 50 | 17 | 45 | 20 | 340 |
| 50 – 60 | 6 | 55 | 30 | 180 |
| Total | `Ʃ f_i = 100` | `Ʃ (f_i × d_i) = 300` |
Let A = 25 be the assumed mean. Then we have:
Mean, x = A + `(sum (f_i xx d_i))/(sum f_i)`
= 25+`300/100`
=28
∴ 𝑥 = 28
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