Correct Answer - Option 4 : None of the above

**Concept:**

The mean of a set of numbers is the sum divided by the number of terms.

mean = \(\rm \frac{sum \: of\: the \: terms}{number\: of \:terms}\)

**Calculation:**

Given the numbers are 4, 6, x, 10, 12, 16

mean is 14

\(\rm 14 = \frac{4 + 6 + x + 10 + 12 + 16 }{6} \)

84 = 48 + x

x = 84 - 48

x = 36

**∴ The value of x is 36**