The median of the following data is: Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 No. of Students: 15, 25, 52, 56, 78, 80, 70a.40.67b.45.13c.47.41d.49.28

To find the median of grouped data, we first need to find the cumulative frequency. The cumulative frequency is the running total of the frequencies. On a graph, it can be represented as a cumulative frequency curve.

Here is the table with the cumulative frequencies:

The total number of students is 376. The median is the value that separates the higher half from the lower half of the data set, so it is the value at the position (n+1)/2 = (376+1)/2 = 188.5th position.

Looking at the cumulative frequency column, the 188.5th position falls in the interval 40-50.

The formula to calculate the median in a grouped frequency distribution is:

Median = L + [ ( (n/2) - CF ) / f ] * c

where: L = lower class boundary of the group containing the median = 40 n = total number of data = 376 CF = cumulative frequency of the group before the median group = 148 f = frequency of the median group = 78 c = width of the interval = 10

Substituting these values into the formula, we get:

Median = 40 + [ ( (376/2) - 148 ) / 78 ] * 10 = 40 + [ (188 - 148) / 78 ] * 10 = 40 + 40/78 * 10 = 40 + 5.13 = 45.13

So, the median of the data is 45.13, which corresponds to option b.