The mean and variance of five observations 2, 4, 9, , are 5 and 6.8 respectively. If M is the mean deviation of these observations about their median, then the value of 10M is equal to

Step-by-step solution

Given the mean is 5 : 2 + 4 + 9 + + 5 = 5 + + 15 = 25 + = 10 Given the variance is 6.8 : 2^2 + 4^2 + 9^2 + ^2 + ^2 5 - 5^2 = 6.8 4 + 16 + 81 + ^2 + ^2 5 - 25 = 6.8 101 + ^2 + ^2 5 = 31.8 101 + ^2 + ^2 = 159 ^2 + ^2 = 58 Using the identity ( + )^2 = ^2 + ^2 + 2 : 10^2 = 58 + 2 2 = 42 = 21 The numbers and are roots of the equation t^2 - 10t + 21 = 0 , which gives t = 3 and t = 7 . So, the five observations are 2, 3, 4, 7, 9 . To find the median, we arrange the data in ascending order: 2, 3, 4, 7, 9 . The median is th