Multiple choice

Class Interval 0-10 10-20 20-30 30-40 40-50 Frequency 12 16 6 7 9 Find the mean of the given distribution.

  1. $22$
  2. $18$
  3. $25$
  4. $9$
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A Correct answer
Explanation

Mean = sum(f*x) / sum(f). Midpoints (x): 5, 15, 25, 35, 45. Frequencies: 12, 16, 6, 7, 9. Sum(f) = 50. Sum(f*x) = (12*5) + (16*15) + (6*25) + (7*35) + (9*45) = 60 + 240 + 150 + 245 + 405 = 1100. Mean = 1100 / 50 = 22.

AI explanation

Using the direct method for grouped data, the mean is calculated as the sum of f_i x_i divided by the sum of f_i, where x_i represents the class marks 5, 15, 25, 35 and 45. The products of frequency and class mark are 60, 240, 150, 245 and 405, which sum to 1100. Dividing this sum by the total frequency of 50 yields a mean of 22.

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