Question

The following table shows the frequency distribution for the number of personal computers sold during the past month in a sample of 40 computer stores located on the island.

Computers sold	Number of stores
4 < 13	6
13 < 22	9
22 < 31	14
31 < 40	7
40 < 49	4

Calculate the mean. Provide your answer to a decimal place.

Answer 1

The following table shows the frequency distribution for the number of personal computers sold during the past month in a sample of 40 computer stores located on the island.

Computers sold	Number of stores
4 < 13	6
13 < 22	9
22 < 31	14
31 < 40	7
40 < 49	4

Above table is a grouped data. Unlike listed data, the individual values for grouped data are not available.

To calculate the mean of grouped data, the first step is to determine the midpoint of each interval, or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean.

In other words, the mean for a population can be found by dividing ∑mf by N, where m is the midpoint of the class and f is the frequency.   

Computers sold or Class Interval	Class Midpoint (m)	Number of stores or Frequency (f)	Product (mf)
4 < 13	(4+13)/2 = 8.5	6	51
13 < 22	(13+22)/2 = 17.5	9	157.5
22 < 31	(22+31)/2 = 26.5	14	371
31 < 40	(31+40)/2 = 35.5	7	248.5
40 < 49	(40+49)/2 = 44.5	4	178
		N = 40	= 1006

Mean of the data,

  

(Rounded to a decimal place)

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