Multiple choice

The arithmetic mean for the following frequency distribution is: | | | | | || |---|---|---|---|---|---| | Class | 0 - 4 | 4 - 8 | 8 - 12 | 12 - 16 | 16 - 20 | | Frequency | 6 | 11 | 20 | 7 | 4 |

  1. 8

  2. 9.2

  3. 9.33

  4. 9.66
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C Correct answer
Explanation

The mean is calculated by finding the sum of (midpoint * frequency) divided by the total frequency. The midpoints are 2, 6, 10, 14, 18, so the sum is (2*6 + 6*11 + 10*20 + 14*7 + 18*4) = (12 + 66 + 200 + 98 + 72) = 448. Dividing 448 by the total frequency of 48 gives 9.33.

AI explanation

Find the midpoints of the classes 0 to 4, 4 to 8, 8 to 12, 12 to 16, and 16 to 20, which are 2, 6, 10, 14 and 18. Multiply each midpoint by its corresponding frequency to get the products 12, 66, 200, 98 and 72. The sum of these products is 448, and the total frequency is 48. The direct mean formula gives the arithmetic mean as 448 divided by 48, which equals 9.33.

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