Question

The list of integers 15, 20, 26, x, y, 32 has a mode of 26 and an arithmetic mean of 27. What is the median of the list of numbers?

23.5

32

15

26

23

Answer 1

The median of the list is 26.

Explanation:

Since the mode of the list is 26, and so far we only have one occurrence of 26 in the list, we know that one of our unknowns must equal 26.

If we set x = 26, we can then solve for y using the arithmetic mean formula. We are left with:
`(15+20+26+26+y+32)/(6) = 27`.

Solving for y leaves us with y=43.

Finally, we can put the list in order and find the middle values. Since the two middle values are 26, the median of the list is 26.