A student was asked to find the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?

Question: A student was asked to find the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?

Solution:
the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x
= (3 + 12 + 7 + 9 + 15 + 13 + 8 + 18 + 17 + 21 + 14 + x )/12
= (137 + x)/12

∴ (137 + x)/12 = 12
⇒ 137 + x = 144
⇒ x = 7