Multiple choice

Read the following data and find the arithmetic mean. |||||||| |---|---|---|---|---|---|---| | (less than) x| 10| 20| 30| 40| 50| 60| | Frequency| 5| 20| 40| 58| 70| 100|

  1. 30.14

  2. 32.43

  3. 35.70

  4. 36.21
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C Correct answer
Explanation

Convert cumulative frequencies to class frequencies: 0-10 (5), 10-20 (15), 20-30 (20), 30-40 (18), 40-50 (12), 50-60 (30). Midpoints: 5, 15, 25, 35, 45, 55. Mean = (5*5 + 15*15 + 20*25 + 18*35 + 12*45 + 30*55) / 100 = (25 + 225 + 500 + 630 + 540 + 1650) / 100 = 3570 / 100 = 35.70.

AI explanation

Convert the given cumulative frequency distribution into a standard frequency distribution. The class frequencies are 5, 15, 20, 18, 12, and 30, which sum to a total frequency of 100. The class marks for the intervals 0 to 10, 10 to 20, 20 to 30, 30 to 40, 40 to 50, and 50 to 60 are 5, 15, 25, 35, 45, and 55, respectively. Multiplying each class mark by its corresponding frequency gives the products 25, 225, 500, 630, 540, and 1650, which sum to 3570. The arithmetic mean is calculated by dividing this sum by the total frequency, so 3570 divided by 100 equals 35.70.

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