Theory question 111
ProbabilityThe table shows the scores obtained when a fair die was thrown a number of times.
Score: 1, 2, 3, 4, 5, 6
Frequency: 2, 5, x, 11, 9, 10
If the probability of obtaining a 3 is 0.26, find the (a) median (b) standard deviation of the distribution.
Show the model answer
Model answer
x/(x + 37) = 0.26 → x = 0.26x + 9.62 → 0.74x = 9.62 → x = 13. Total = 50.
(a) Median = average of 25th and 26th scores. Cumulative frequencies: 2, 7, 20, 31, … so both are 4: median = 4.
(b) Mean = (2 + 10 + 39 + 44 + 45 + 60)/50 = 200/50 = 4.
Σf(x − 4)2 = 2(9) + 5(4) + 13(1) + 11(0) + 9(1) + 10(4) = 100.
SD = √(100/50) = √2 ≈ 1.41.
Explanation
Find x first from the probability, then use the full table.