Mathematics
The distribution table given below shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.
| Marks obtained | No. of students |
|---|---|
| 5 | 3 |
| 6 | 9 |
| 7 | 6 |
| 8 | 4 |
| 9 | 2 |
| 10 | 1 |
Measures of Central Tendency
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Answer
The variates (marks) are already in ascending order. We construct the cumulative frequency table as under :
| Marks (xi) | No. of students (fi) | Cumulative frequency (C.F.) | fixi |
|---|---|---|---|
| 5 | 3 | 3 | 15 |
| 6 | 9 | 12 | 54 |
| 7 | 6 | 18 | 42 |
| 8 | 4 | 22 | 32 |
| 9 | 2 | 24 | 18 |
| 10 | 1 | 25 | 10 |
| Total | 25 | 171 |
Mean = = 6.84.
Total number of observations = 25, which is odd.
All observations from 13th to 18th are equal, each = 7, so median = 7.
As the variate 6 has maximum frequency 9, so mode = 6.
Hence, mean = 6.84, median = 7 and mode = 6.
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