Multiple choice

$x$ $10$ $20$ $30$ $40$ $50$ $f$ $5$ $7$ $15$ $13$ $10$ From the given distribution, calculate mean deviation about mean.

  1. $1.021$
  2. $11.231$
  3. $10.256$
  4. $12.214$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mean = sum(f*x) / sum(f) = (50+140+450+520+500) / 50 = 1660 / 50 = 33.2. Mean deviation = sum(f * |x - mean|) / sum(f). |10-33.2|=23.2, |20-33.2|=13.2, |30-33.2|=3.2, |40-33.2|=6.8, |50-33.2|=16.8. Sum = (5*23.2 + 7*13.2 + 15*3.2 + 13*6.8 + 10*16.8) = 116 + 92.4 + 48 + 88.4 + 168 = 512.8. Mean deviation = 512.8 / 50 = 10.256.

AI explanation

The sum of the frequencies is 5 + 7 + 15 + 13 + 10 = 50. The sum of the products of the frequency and value is (5)(10) + (7)(20) + (15)(30) + (13)(40) + (10)(50) = 1640. The mean is 1640 / 50 = 32.8. The absolute deviations from the mean are 22.8, 12.8, 2.8, 7.2, and 17.2, and their sum multiplied by the respective frequencies is (5)(22.8) + (7)(12.8) + (15)(2.8) + (13)(7.2) + (10)(17.2) = 512.8. The mean deviation is 512.8 / 50 = 10.256. The mean deviation about the mean is 10.256.

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