Question

Ray is 2 inch taller than Lin, and Ray is 3 inch taller than Sam. What is the average height of ray, Lin and Sam? The median height of Ray, Lin and Sam?

Answer 1

The answer is: the average height is $r-\frac{5}{3}$, the median height is r-2.

r - Ray's height
l - Lin's height
s - Sam's height

Ray is 2 inch taller than Lin:   r = l + 2          ⇒ l = r - 2
Ray is 3 inch taller than Sam: r = s + 3         ⇒ s = r - 3

The average is the sum of all values divided by the number of values:
$A= \frac{r + l + s}{3}$
Since l = r - 2 and s = r - 3, then:
$A= \frac{r + (r-2) + (r-3)}{3} = \frac{r+r-2+r-3}{3} = \frac{3r-5}{3} = \frac{3r}{3} - \frac{5}{3} =r-\frac{5}{3}$

The median means the middle value. Let's first rearrange values so we can find the middle one:
Ray is taller than Lin and Sam, so Ray is the tallest.
Sam is much shorter than Ray comparing to Lin, so Sam is the shortest.
Therefore, values are from the lowest to the highest:
(s, l, r)
⇒ (r-3, r-2, r)
Median of these values is in the middle, so the median height is r-2.