Multiple choice

Score 10-20 20-30 30-40 40-50 50-60 60-70 frequency 12 3 3 2 10 10 Find the mean of the following data:

  1. $40.5$
  2. $41.25$
  3. $42.45$
  4. $43.9$
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B Correct answer
Explanation

Midpoints: 15, 25, 35, 45, 55, 65. Frequencies: 12, 3, 3, 2, 10, 10. Sum of f*x = 180 + 75 + 105 + 90 + 550 + 650 = 1650. Total frequency = 40. Mean = 1650 / 40 = 41.25.

AI explanation

Using the direct method for grouped data, the mean is the sum of (midpoint times frequency) divided by the total frequency. The midpoints are 15, 25, 35, 45, 55, and 65. The sum of frequency times midpoint is (12*15) + (3*25) + (3*35) + (2*45) + (10*55) + (10*65) = 180 + 75 + 105 + 90 + 550 + 650 = 1650. The total frequency is 12 + 3 + 3 + 2 + 10 + 10 = 40. Dividing 1650 by 40 gives a mean of 41.25.

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