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

1 Answer
Alan P.
Oct 21, 2015

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.

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