A set of numbers {10, 21, 17, 12, x} has the property that the mean is equal to the median.

What could the value of x be?

The set can be ordered in 5 possible ways:
{x, 10, 12, 17, 21}
{10, x, 12, 17, 21}
{10, 12, x, 17, 21}
{10, 12, 17, x, 21}
{10, 12, 17, 21, x}

The three possible medians are: 12, x, and 17.
The average is (x+60)/5.

When the median is 12, x<=12.
Then, (x+60)/5=12 which yields x=0, which is compatible with x<=12. Thus, x=0 is a solution.

When the median is x, 12<=x<=17.
Then, (x+60)/5=x which yields x=15, which is compatible with 12<=x<=17. Thus, x=15 is a solution.

When the median is 17, x>=17.
Then, (x+60)/5=17 which yields x=25, which is compatible with x>=17. Thus, x=25 is a solution.

In summary, the three possible values for x are: 0, 15 and 25.

Posted by Kurious on 2007-04-20 11:36:51