0. 7. 2. 6. 9. 2. 0. 7.

Two more numbers are added. The median is 3.5 and the mode is 0.

What are the numbers ?

I started by putting the numbers in order:

0. 0. 2. 2. 6. 7. 7. 9

One must be 0 for the mode to be 0? But how do I work out the other using the median?

Walthamx
May 28, 2018

#1**0 **

Your hypothesis is correct. One must be 0 for the mode to be 0.

So now the numbers are **0 0 0 2 2 6 7 7 9**.

If one more number is added, the number of integers in the list will be 10.

Let x be the other integer.

The numbers are **0 0 0 2 2 6 7 7 9 x**.(I don't know the value of x, without loss of generality, I put it at the back of the list.)

Now the mode apparently is not 3.5, Therefore x should be added right after the left half of the list. (why?)

So the numbers now are **0 0 0 2 2 x 6 7 7 9**.

Next thing we do is to solve \(\dfrac{2+x}{2} = 3.5\)

Just by inspection, x = 5.

Therefore the 2 numbers added are **0 and 5**.

MaxWong
May 28, 2018