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 mean of this set is (60 + x)/5.

The median must be identical to one of the members of the set, since there are an odd number (5) of members. This means there are five possible medians, each of which determines a different value for x, given that mean and median are equal.

Case 1:
Median: 10
Mean: (60 + x)/5 = 10
          60 + x = 50
          x = -10

Case 2:
Median: 12
Mean: (60 + x)/5 = 12
          60 + x = 60
          x = 0

Case 3:
Median: 17
Mean: (60 + x)/5 = 17
          60 + x = 85
          x = 25

Case 4:
Median: 21
Mean: (60 + x)/5 = 21
          60 + x = 105
          x = 45

Case 5:
Median: x
Mean: (60 + x)/5 = x
          60 + x = 5x
          60 = 4x
          x = 15

Posted by Jyqm on 2007-04-20 11:04:50