# The mean, median, and mode are all equal for this set: (3,4,5,8,x). What's the value of 'x'?

Apr 22, 2018

$x = 5$

#### Explanation:

$3 , 4 , 5 , 8 , x$

mean$=$mode$=$median

$\sum {x}_{i} = \frac{20 + x}{5} = 4 + \frac{x}{5}$

since we required there to be a mode

$\therefore x > 0$

$\because x = 0 \implies \overline{x} = 4 , \text{ median " =4" but there is no mode}$

$x = 5 \implies \overline{x} = 4 + \frac{5}{5} = 5$
we have

$3 , 4 , 5 , 5 , 8$

median$= 5$

mode $= 5$

$\therefore x = 5$