In the list S = {17, 9, 24, X, 14, 17, 21} the mean, median and mode are all equal to one another. What is the value of X?

Question: In the list S = {17, 9, 24, X, 14, 17, 21} the mean, median and mode are all equal to one another. What is the value of X?

Solution:
Let the list be: 9, 14, 17, 17, 21, 24, X (sorted, except X).
Since mean = median = mode, and mode = 17 (appears twice, others once),
⇒ mean = median = 17.

We know,
Mean = (sum of all numbers)/7 = 17
17 = (17 + 9 + 24 + X + 14 + 17 + 21)/7
⇒ 17 = (102 + X)/7
⇒ 102 + X = 119
⇒ X = 119 - 102
∴ X = 17

So the value of X is 17.