Multiple choice

Consider the following distribution: | Class | Frequency | | --- | --- | | 0 – 20 | 17 | | 20 – 40 | 28 | | 40 – 60 | 32 | | 60 – 80 | f | | 80 – 100 | 19 | If the mean of the above distribution is 50, then what is the value of f?

  1. 24

  2. 34

  3. 56

  4. 96
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A Correct answer
Explanation

Mean = Sum(f*x) / Sum(f). Midpoints are 10, 30, 50, 70, 90. Sum(f*x) = 170 + 840 + 1600 + 70f + 1710 = 4320 + 70f. Sum(f) = 17+28+32+f+19 = 96+f. (4320+70f)/(96+f) = 50. 4320+70f = 4800+50f. 20f = 480. f = 24.

AI explanation

The sum of the midpoints multiplied by their respective frequencies is (17*10) + (28*30) + (32*50) + (f*70) + (19*90), equaling 170 + 840 + 1600 + 70f + 1710 = 4320 + 70f. The total frequency is 17 + 28 + 32 + f + 19 = 96 + f. Setting the mean equation, (4320 + 70f) / (96 + f) = 50, gives 4320 + 70f = 4800 + 50f. Solving 20f = 480 results in f = 24.

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