Question

From the list of numbers below, write one number in each box. You may use each number exactly once. 3, 4, 7, 8, 9, 14.

Three Numbers with a mean=8 and MAD=4

Answer 1

Answer: 3, 7 and 14

Explanation:

We want 3 numbers with a mean of 8, and a MAD of 4.

if we have the numbers a, b and c.

The mean is:

M = (a + b + c)/3

MAD = ( Ia - MI + Ib - MI + Ic - MI)/3

now, we know that M = 8 and MAD = 4, so we can replace those values:

8 = (a + b + c)*/3

3*8 = 24 = a + b + c

and

4 = ( Ia - 8I + Ib - 8I + Ic - 8I)/3

4*3 = 12 = Ia - 8I + Ib - 8I + Ic - 8I

So now we have the two equations:

24 = a + b + c

12 = Ia - 8I + Ib - 8I + Ic - 8I

Let's took the numbers 3, 7 and 14

I selected those because are the numbers where the distance between them is the biggest, and they add up to 24, and you can see that the MAD is a big number, which implies that our 3 numbers are not close between them.

3 + 7 + 14 = 10 + 14 = 24

and for the MAD

I3 -8I + I7 - 8I + I14 - 8I = 5 + 1 + 6 = 12

So the correct options are 3, 7 and 14