Theory question 112
StatisticsIf the mean and standard deviation of the numbers x, 2.5, 4, y and 7 are 4 and √(31/10) respectively. Find the values of x and y where x < y.
Show the model answer
Model answer
Mean: (x + 2.5 + 4 + y + 7)/5 = 4, so x + y = 6.5.
Variance 3.1: Σ(value − 4)² = 15.5; (2.5 − 4)² + 0 + 3² = 11.25, so (x − 4)² + (y − 4)² = 4.25.
With y = 6.5 − x: 2x² − 13x + 18 = 0, (2x − 9)(x − 2) = 0.
x = 2, y = 4.5 (since x < y).
Explanation
Use the mean to link x and y, then the variance to get a quadratic.