Class-Mark Method: Mean of Grouped Data

For grouped data, the class mark $x_i$ is the average of the lower and upper class limits. The mean is then $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$. For class 0-10 the class mark is 5, for 10-20 it is 15, and so on.

Slide the frequencies $f_1, f_2, f_3$ of three classes. The lab computes class marks, the products $f_i x_i$, the totals, and the mean instantly. Try equal frequencies to see the mean sit at the middle class mark.

Students take the lower limit as the class mark, not the midpoint. Also, dividing by 3 (number of classes) instead of $\sum f_i$ (total frequency) is a common slip. Always sum frequencies first.

Census reports show population in age groups like 0-10, 10-20, 20-30 years. Computing the mean age of a village this way is faster than listing every person. The lab mirrors this workflow with three classes.