Mathematics
Calculate mean, median and mode of the following distribution :
| Marks | Frequency |
|---|---|
| 3 | 3 |
| 4 | 5 |
| 5 | 8 |
| 6 | 7 |
| 7 | 9 |
| 8 | 4 |
| 9 | 3 |
| 10 | 1 |
Statistics
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Answer
Cumulative frequency distribution :
| Marks (x) | Frequency (f) | Cumulative frequency | fx |
|---|---|---|---|
| 3 | 3 | 3 | 9 |
| 4 | 5 | 8 (5 + 3) | 20 |
| 5 | 8 | 16 (8 + 8) | 40 |
| 6 | 7 | 23 (7 + 16) | 42 |
| 7 | 9 | 32 (9 + 23) | 63 |
| 8 | 4 | 36 (4 + 32) | 32 |
| 9 | 3 | 39 (3 + 36) | 27 |
| 10 | 1 | 40 (1 + 39) | 10 |
| Total | Σf = 40 | Σfx = 243 |
By formula,
Mean = = 6.075
Given,
Total terms = 40, which is even.
By formula,
Median = = 20th term.
From table,
Marks of 17th to 23rd term = 6.
∴ Median = 6.
Highest frequency is of 7 marks.
∴ Mode = 7.
Hence, mean = 6.075, median = 6 and mode = 7.
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