S = {16, 9 ,23, X, 13, 16}. In list S, the mean, median and mode are all equal to one another. What is the value of X ?

Explanation: Arranging the number is ascending order without X, we get \(9, 13, 16, 16, 23\). If there are odd number of numbers, the median is the one in the middle when arranged in ascending or descending order. If there are even number of numbers, the median is the average of the 2 numbers in the middle when arranged in ascending or descending order. Mode is the number that occurs most frequently. So, X cannot be equal to 15 , because then mode would be 16 and median would be 15.5 . So, option A can be omitted If \(x=16\), median = mode, but mean is \((9+13+16+16+16+23)/6=15.5\). So, option B can be omitted So, X must be greater than 16 . Which means, since mean=median=mode, it can be only one number, hence the mean is 16. Now, mean is 16 . So, \(\frac{9+13+16+16+23+X}{6} = 16 \Rightarrow 77 + X = 96 \Rightarrow X=19\). Here, mean=median=mode. So, answer is option C.