If the mean and median are equal for the set {4, 8, x}, what can you say about the value of x?

Answer 1

You may not assume the data set is sorted.

case 1: x < 4

then the median is 4, so (x+4+8)/3 = 4 , since the mean equals the median.

Then, (x+12)/3 = 4

x+12 = 12

x = 0

case 2: 4 < x < 8.

so (4+x+8)/3 = x, since the mean equals the median.

then, (x+12)/3 = x

x+12 = 3x

12 = 2x

x = 6

case 3: x>8

then the median is 8, so (x+4+8)/3 = 8 since the mean equals the median.

(x+12)/3 = 8

x+12 = 24

x = 12