The time (unit: minutes) that someone spends on the way to work five times are x, y, 10, 11 and 9 respectively. Given that the average of this set of data is 10 and the variance is 2, then the value of | X-Y | is () A. 1B. 2C. 3D. 4

The time (unit: minutes) that someone spends on the way to work five times are x, y, 10, 11 and 9 respectively. Given that the average of this set of data is 10 and the variance is 2, then the value of | X-Y | is () A. 1B. 2C. 3D. 4

From the mean value of this set of data is 10 and the variance is 2, we can get: x + y = 20, (X-10) 2 + (Y-10) 2 = 8. To solve the equations, we need some skills, because we don't need to find X and Y directly, just find | X-Y |, let x = 10 + T, y = 10-T, let (X-10) 2 + (Y-10) 2 = 8 get T2 = 4; | X-Y | = 2 | t | = 4, so we choose D