Calculating the Median from the Given Data

To calculate the median from the given data, we need to follow these steps:

1. Arrange the data in ascending order:
- Marks: 0-20, 20-40, 40-60, 60-80, 80-100
- No. of students: 5, 15, 30, 8, 2

Arranging the data in ascending order gives us:
- Marks: 0-20, 20-40, 40-60, 60-80, 80-100
- No. of students: 2, 5, 8, 15, 30

2. Calculate the cumulative frequency:
Cumulative frequency is the sum of the frequencies up to a certain point. To calculate it, we start from the first frequency and keep adding the subsequent frequencies.

The cumulative frequency for the given data is:
- Marks: 0-20, 20-40, 40-60, 60-80, 80-100
- Cumulative frequency: 2, 7, 15, 30, 60

3. Identify the median class:
The median class is the class interval that contains the median value. To find the median class, we divide the total number of observations by 2 and locate the class corresponding to this value in the cumulative frequency.

The total number of students is 60 (sum of all frequencies).
The median class is the class interval that contains the 30th observation (60/2 = 30).

From the cumulative frequency, we can see that the median class is 40-60, as it contains the 30th observation.

4. Calculate the median:
The median can be calculated using the formula:

Median = Lower boundary of median class + [(n/2) - Cumulative frequency of the class] * Width of the class / Frequency of the median class

In this case, the lower boundary of the median class is 40, the cumulative frequency of the class is 15, the width of the class is 20, and the frequency of the median class is 30.

Substituting these values into the formula, we get:
Median = 40 + [(30/2) - 15] * 20 / 30
Median = 40 + (15 - 15) * 20 / 30
Median = 40

Conclusion:
The median of the given data is 40. This means that 50% of the students have marks below 40, and 50% of the students have marks above 40.