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?

This problem has three solutions.

Upon examination of the first four numbers, it is determined that only two of the four (12 & 17) could possibly be a median.  The numbers 10 and 21 cannot because each already has three other numbers either below or above it.  This leaves three possible medians as 12, 17, or x.

Now it becomes a series of three solvable equations.  Substituting 60 for (10 + 12 + 17 + 21):

• (x + 60)/5  =  12
• (x + 60)/5  = x
• (x + 60)/5  = 17

The three solutions are x = {0,15,25}

Posted by hoodat on 2007-04-20 13:38:01