The average of 15 numbers is 15. If the average of the first five numbers is 14 and that of the other 9 numbers is 16, then find the middle number.

Average of 15 numbers = 15, Average of 5 numbers = 14, Average of 9 numbers = 16

Average = Total numbers/Number of Numbers
15 = Total numbers/15
Therefore, total numbers = 15 x 15 = 225.

Middle number = (Total numbers) – [(Average of 5 num x no of num) + ( Average of 9 num x no of num)]
= (225) – [(14 x 5) + (16 x 9)]
= (225) – (214)
= 11.