Theory question 111
ProbabilityThe table shows the distribution of outcomes when a die is thrown 50 times.
Scores: 1, 2, 3, 4, 5, 6
Frequency: 2, 5, 13, 11, 9, 10
Calculate the: (a) mean deviation of the distribution; (b) probability that a score selected at random is at least a 4.
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Model answer
(a) Σfx = 2 + 10 + 39 + 44 + 45 + 60 = 200, so the mean = 200/50 = 4.
|x − 4|: 3, 2, 1, 0, 1, 2. Σf|x − 4| = 6 + 10 + 13 + 0 + 9 + 20 = 58.
Mean deviation = 58/50 = 1.16.
(b) Scores 4, 5, 6: 11 + 9 + 10 = 30. Probability = 30/50 = 3/5 (0.6).
Explanation
Mean deviation is the average distance of the scores from the mean.