Let the data 4, 10, x, y, 27 be in increasing order. If the median of the data is 18 and its mean deviation about mean is 7.6, then the mean of this data, is

The median of the given data is x and it is given that the median is 18. Therefore, x = 18. Let X be the mean. It is given that the mean deviation about mean is 7.6 and mean is less than the median i.e. X < 18.∴ X¯=4+10+18+y+275and (X¯−4)+(X¯−10)+(18−X¯)+(y−X¯)+(27−X¯)5=7.6 ⇒ 5X¯−y=59 and, y−X¯=7 ⇒ X¯=16.5