Theory question 112
StatisticsThe data shows the ordered marks scored by students in a test: 11, 12, (2x + y), (x + 2y), 14 and (y2 − 2x). Given that the median is 13½ and y is greater than x by 1, find: (a) the values of x and y; (b) correct to three significant figures, the standard deviation of the distribution.
Show the model answer
Model answer
(a) Six marks: median = ½[(2x + y) + (x + 2y)] = 13½, so x + y = 9. With y = x + 1: x = 4, y = 5.
(b) Marks: 11, 12, 13, 14, 14, 17. Mean = 81/6 = 13.5.
Squared deviations: 6.25, 2.25, 0.25, 0.25, 0.25, 12.25; sum 21.5.
SD = √(21.5/6) = √3.583 ≈ 1.89.
Explanation
With an even number of values, the median is the mean of the middle two.