A students was asked to find the arithmetic mean of the numbers 2, 9, 13, 17, 11, 5, 12, 18, 14, 8, 15 and x. He found the mean to be 13. What should be the number in place of x?
1). 3
2). 7
3). 17
4). 32
We know that,
Arithmetic mean = (Sum of all terms)/(Number of terms)
According to the given information, the arithmetic mean given 12 numbers is 13.
∴ 13 = (2 + 9 + 13 + 17 + 11 + 5 + 12 + 18 + 14 + 8 + 15 + x)/12
⇒ 13 = (124 + x)/12
∴ 124 + x = 13 × 12
∴ x = 156 – 124 = 32