Multiple choice

Find the mean of the following data: | Age group | 40 – 44 | 45 – 49 | 50 – 54 | 55 – 59 | 60 – 64 | 65 – 69 | | --- | --- | --- | --- | --- | --- | --- | | Number of people | 3 | 8 | 13 | 11 | 9 | 6 |

  1. 44.3

  2. 48.9

  3. 51.7

  4. 55.3

  5. 56.6
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D Correct answer
Explanation

Midpoints (x): 42, 47, 52, 57, 62, 67. Frequencies (f): 3, 8, 13, 11, 9, 6. Sum (f*x): 126 + 376 + 676 + 627 + 558 + 402 = 2765. Total frequency = 50. Mean = 2765 / 50 = 55.3.

AI explanation

Adjust the discontinuous class intervals by subtracting 0.5 from the lower limits and adding 0.5 to the upper limits, giving intervals like 39.5 to 44.5. The midpoints are 42, 47, 52, 57, 62, and 67, and multiplying these by the frequencies gives the products 126, 376, 676, 627, 558, and 402. The total number of people is 50 and the sum of the products is 2765, so dividing 2765 by 50 gives a mean of 55.3.

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