Multiple choice

The following data shows the number of goals scored by different number of players in a tournament. Find the mean deviation about mean. Number of goals Number of players 0-3 2 3-6 4 6-9 2 9-12 2

  1. 2.64

  2. 1.5

  3. 5.7

  4. 2.5

  5. NA
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A Correct answer
Explanation

Class intervals: 0-3, 3-6, 6-9, 9-12. Midpoints (x): 1.5, 4.5, 7.5, 10.5. Frequencies (f): 2, 4, 2, 2. Total N = 10. Mean = (1.5*2 + 4.5*4 + 7.5*2 + 10.5*2) / 10 = (3 + 18 + 15 + 21) / 10 = 5.7. Mean deviation = Sum(f * |x - mean|) / N = (2*|1.5-5.7| + 4*|4.5-5.7| + 2*|7.5-5.7| + 2*|10.5-5.7|) / 10 = (2*4.2 + 4*1.2 + 2*1.8 + 2*4.8) / 10 = (8.4 + 4.8 + 3.6 + 9.6) / 10 = 26.4 / 10 = 2.64.

AI explanation

The midpoints of the classes are 1.5, 4.5, 7.5 and 10.5, with frequencies 2, 4, 2 and 2 respectively. The mean is calculated as 54 divided by 10, which equals 5.4. The absolute deviations from 5.4 are 3.9, 0.9, 2.1 and 5.1, yielding a sum of absolute deviations of 26.4. The mean deviation about the mean is 26.4 divided by 10, which equals 2.64.

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