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In order to compute the average of a grouped data set, the first step is to find the midpoint () of each class, which is defined as

Then, the population mean and the sample average are defined as follows:

(2.6.1)

(2.6.2)

Here, summation is over the number of classes involved, midpoint of the ith class, frequency of the ith class, that is, the number of values falling in the ith class, population size, and sample size.

Example 2.6.1 (Ages of basketball fans) Find the mean of the grouped data that is the frequency distribution of a group of 40 basketball fans watching a basketball game (see Table 2.6.1).

Solution: Using formula (2.6.2), we have

Table 2.6.1 Age distribution of a group of 40 basketball fans watching a basketball game.

Class	Frequency ()	Class midpoint ()
	8	(10+20)/2 = 15	120
	10	(20+30)/2 = 25	250
	6	(30+40)/2 = 35	210
	11	(40+50)/2 = 45	495
	5	(50+60)/2 = 55	275