Mathematics
Mathematics
Problem
The cumulative frequencies for a set of test marks are given below. Class (marks): 30–40, 40–50, 50–60, 60–70 Cumulative frequency: 7, 18, 30, 40 Calculate the mean mark of the students.Intuitive explanation
To find the mean from grouped data, you need to recover the actual frequency in each class interval, then use the class midpoint as a representative value for that interval. The key insight is that cumulative frequency tells you totals, so you subtract consecutive values to get how many students actually scored in each band—then multiply each midpoint by its frequency, sum those products, and divide by the total number of students.
Intuitive explanation
To find the mean from grouped data, you need to recover the actual frequency in each class interval, then use the class midpoint as a representative value for that interval. The key insight is that cumulative frequency tells you totals, so you subtract consecutive values to get how many students actually scored in each band—then multiply each midpoint by its frequency, sum those products, and divide by the total number of students.