If the mean of 4,7,2,8,6 and a is 7 , then the mean deviation from the median of these observations is

Step-by-step solution

Given observations are 4, 7, 2, 8, 6, a and mean is 7. We know aligned & Mean = 4+7+2+8+6+a 6 & 7= 4+7+2+8+6+a 6 a=15 aligned Now, given observations can be written in ascending order which is 2,4,6,7,8,15 Since, No. of observation is even Median = ( 6 2 ) th observation + ( 6 2 +1 ) th observation 2 = 3rd observation +4 th observation 2 = 6+7 2 = 13 2 aligned & Now, Mean deviation = _ i=1 ^6 |x_i- 13 2 | 6 & = |4- 13 2 |+ |7- 13 2 |+ |2- 13 2 |+ |8- 13 2 |+ |6- 13 2 |+ |15- 13 2 | 6 & = 5 2 + 1 2 + 9 2 + 3 2 + 1 2