Problem

A survey was taken, asking 60 people about the number of books they read in a year. The number of books read were divided into 5 groups: 0-10, 11-20, 21-30, 31-40, 41-50. The number of people in each group were 10, 15, 12, 15, 8 respectively. What are the midpoints of each group in the frequency distribution table, and what is the average number of books read by the survey participants based on these midpoints and frequencies?

Answer

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Answer

The total frequency is 60. Therefore, the mean number of books read is \(1485\, / \,60 = 24.75\).

Steps

Step 1 :First, we calculate the midpoints of each group. The midpoint is calculated as \((lower \, limit + upper \, limit) \, / \, 2\).

Step 2 :For the group 0-10, the midpoint is \((0+10)\,/\,2 = 5\).

Step 3 :For the group 11-20, the midpoint is \((11+20)\,/\,2 = 15.5\).

Step 4 :For the group 21-30, the midpoint is \((21+30)\,/\,2 = 25.5\).

Step 5 :For the group 31-40, the midpoint is \((31+40)\,/\,2 = 35.5\).

Step 6 :For the group 41-50, the midpoint is \((41+50)\,/\,2 = 45.5\).

Step 7 :Next, we find the weighted average, or mean, by multiplying each midpoint by its frequency, summing these products, and dividing by the total frequency.

Step 8 :The sum of the products is \(5*10 + 15.5*15 + 25.5*12 + 35.5*15 + 45.5*8 = 50 + 232.5 + 306 + 532.5 + 364 = 1485\).

Step 9 :The total frequency is 60. Therefore, the mean number of books read is \(1485\, / \,60 = 24.75\).

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