Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.)

What is the smallest the average of those ten integers could be?

P.S. When you are answering, please include equations. Not just the answer.

skc123 Jan 24, 2021

#1**+1 **

_ _ _ 10 _ _ _ three integers below 10 three above 10 choose the smallest possible to make the average as small as possib;e

123 10 11 12 13 av =7.42

Guest Jan 24, 2021

#2**+1 **

If the median of an even number of distinct integers is ten, then the two middle numbers have to sum to 20.

Making them 9 and 11 would be ideal so we can use the rest of the small one-digit numbers for the below numbers and the small two-digit numbers directly above 11(what I'm saying is using these numbers will minimize the other numbers)

To minimize the others, we make them 1, 2, 3, 4, 9, 11, 12, 13, 14, and 15.

The average of those numbers is 84/10 or 8.4.

MooMooooMooM Jan 24, 2021

#6**0 **

Hey, MooMoo, look at my answer posted just below yours a few seconds later.

Great minds think alike .... and so do ours!

_{.}

Guest Jan 24, 2021

#7**+1 **

wow i saw it,

same answer, kind of the same explantion,

Great mind do think alike!

MooMooooMooM
Jan 24, 2021

#3**+1 **

*Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.) What is the smallest the average of those ten integers could be?*

*P.S. When you are answering, please include equations. Not just the answer.*

I don't have an equation, but I'll include my reasoning. Maybe you can make the equations.

The median is the integer that the number of integers smaller than it is equal to the number of intergers larger than it. To get the smallest average, we'll need the smallest integers. Since there's an even number of integers in the list, the median has to fall between two integers. 9 and 11 are the smallest that will give us 10.

Now you just use the smallest numbers that include those two. I get 1, 2, 3, 4, 9, 11, 12, 13, 14, 15.

The integers in that list total 84 so the average of them is **8.4**.

_{.}

Guest Jan 24, 2021

#8**0 **

**Attn: skc123,**

Do not ask a question more than once in a short space of time.

If you do repost after a day or two then you get the address of the old post and ask for it to be answered there.

This is the 3rd time you have asked this question in the space of about 1 hour.

DO NOT WASTE PEOPLE'S TIME LIKE THIS AGAIN!

Melody Jan 24, 2021