Multiple choice

Find the mean of the following frequency distribution: Age (in years) $18$ $19$ $20$ $21$ $22$ No. of boys $14$ $10$ $20$ $24$ $12$

  1. $19.125$ years
  2. $20.125$ years
  3. $21.125$ years
  4. $21.175$ years
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B Correct answer
Explanation

Mean = Sum(f*x) / Sum(f). Sum(f*x) = 18*14 + 19*10 + 20*20 + 21*24 + 22*12 = 252 + 190 + 400 + 504 + 264 = 1610. Sum(f) = 14+10+20+24+12 = 80. Mean = 1610 / 80 = 20.125.

AI explanation

To find the mean of this frequency distribution, multiply each age by its corresponding number of boys and divide by the total number of boys. The sum of the products is (18 * 14) + (19 * 10) + (20 * 20) + (21 * 24) + (22 * 12), which equals 252 + 190 + 400 + 504 + 264 = 1610. The total number of boys is 14 + 10 + 20 + 24 + 12 = 80. Dividing the total sum by the number of boys gives 1610 / 80 = 20.125 years.

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