Calculate the mean and median the following data ... - Free Printable

1. Calculate the mean:
- Sum of (marks × number of students): \(10 \times 3 + 11 \times 5 + 12 \times 4 + 13 \times 5 + 14 \times 2 + 16 \times 3 + 19 \times 2 + 20 \times 1 = 332\)
- Total number of students: \(3 + 5 + 4 + 5 + 2 + 3 + 2 + 1 = 25\)
- Mean: \(\frac{332}{25} = 13.28\)

2. Determine the median:
- Since \(n = 25\) (odd), the median is the \(\left(\frac{25 + 1}{2}\right)\)th term, which is the 13th term.
- Arrange the data in ascending order and find the 13th term: The cumulative frequencies are 3, 8, 12, 17, 19, 22, 24, 25. The 13th term falls in the 13th mark.
- Median: 13

3. Calculate the mode using the empirical formula:
- Empirical formula: Mode = \(3 \times \text{Median} - 2 \times \text{Mean}\)
- Mode = \(3 \times 13 - 2 \times 13.28 = 39 - 26.56 = 12.44\)

4. Conclusion:
- The correct answer is 12.44.