Mathematics
The following table gives marks scored by students in an examination :
| Marks | Number of students |
|---|---|
| Less than 5 | 3 |
| Less than 10 | 10 |
| Less than 15 | 25 |
| Less than 20 | 49 |
| Less than 25 | 65 |
| Less than 30 | 73 |
| Less than 35 | 78 |
| Less than 40 | 80 |
Calculate the mean marks correct to 2 decimal places.
Measures of Central Tendency
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Answer
We construct the following table, taking assumed mean a = 17.5. Here, c (width of each class) = 5.
| Marks | Frequency (fi) | Class mark (yi) | ui = (yi - a)/c | fiui |
|---|---|---|---|---|
| 0-5 | 3 | 2.5 | -3 | -9 |
| 5-10 | 7 | 7.5 | -2 | -14 |
| 10-15 | 15 | 12.5 | -1 | -15 |
| 15-20 | 24 | a = 17.5 | 0 | 0 |
| 20-25 | 16 | 22.5 | 1 | 16 |
| 25-30 | 8 | 27.5 | 2 | 16 |
| 30-35 | 5 | 32.5 | 3 | 15 |
| 35-40 | 2 | 37.5 | 4 | 8 |
| Total | ∑ fi = 80 | ∑fi ui = 17 |
By formula,
Hence, mean marks scored by the students is 18.56
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