If the mean, median, and mode are all equal for the set {3,4,5,8,x}, what is the value of x?

Aug 20, 2016

$x = 5$

Explanation:

1st question to ask would be, " Are the values in order?"

Clearly they can't be because then $x$ would have to be equal to 8 in order to have a mode of 8. But while 8 could be the mode, it is not the median.

2nd question " Where must $x$ lie?"

The mode will have to be equal to the median. (the middle value).

This would lead to {3,4,5 ,x ,8} $\Rightarrow$ {3,4,5, 5 ,8}

What about the mean? If $x = 5$, the sum of the numbers = 25.

Mean = $\frac{25}{5} = 5$