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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
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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

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