Question

What combination of seven numbers has a mean of 45, median of 40, and a mode 50?

Answer 1

There are many possible solutions:
`{10,20,30,40,50,50,115}` and `{32,33,35,40,50,50,75}`
are two possibilities

Explanation:

Arranged in ascending order we know that the middle term must be `40` (since it is the median).

The sum of the terms must be `7xx45 = 315`

Two of the terms must be `50`, the mode (we can't have Three terms `=50` since this would require the the three smallest terms to have an average value greater than `40`.

So we have a requirement:
`color(white)("XXX"){ a, b, c, 40, 50, 50, z}`
where `a < b < c < 40 < 50 < z`
and `a+b+c+z = 315 - (40+50+50) = 175`

There are lots of solutions which meet this requirement.