Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a > b) , are 40 and 21 , respectively. If the mean deviation about the median is 26 , then 2a is equal to:

Step-by-step solution

The given numbers are 21, 8, 17, a, 51, 103, b, 13, 67 . There are 9 numbers in total. Given that the mean is 40 , the sum of the numbers is: x_i = 9 40 = 360 The sum of the known numbers is: 21 + 8 + 17 + 51 + 103 + 13 + 67 = 280 Therefore, the sum of a and b is: a + b = 360 - 280 = 80 The median of the 9 numbers is 21 . Arranging the known numbers in ascending order, we get: 8, 13, 17, 21, 51, 67, 103 There are 3 numbers less than 21 and 3 numbers greater than 21 . For 21 to be the median (the 5^ th observation),