Mathematics
The distribution 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
Cumulative frequency distribution table :
| Marks obtained (x) | No. of students (f) | Cumulative frequency | fx |
|---|---|---|---|
| 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 | Σf = 25 | Σfx = 171 |
By formula,
Mean = = 6.84
Here, n = 25, which is odd.
Median = th term
= = 13th term.
From table,
Marks obtained by 13th to 18th student = 7.
Median = 7.
From table,
6 marks has highest frequency.
Mode = 6.
Hence, mean = 6.84, median = 7 and mode = 6.
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