Count if there are more smaller or larger number in a result made of multiple Xs?

Question

Firstly, I am not a math pro or something. So far I was able to use math for my needs, but now I am at my wits' ends. Here is the deal.

These things are known to me:

Avg 1,234, High 2,740, Low 548

Q: Can I know if more numbers which made the Avg result are below the Avg value or above it?

Now, let me explain what part is known and what is unknown.

• I know the max number and the min nuber all the time.

• The Avg value is average of all numbers.

• I always know how many numbers are in the game. In this case there are 22 numbers, but some of them can be 0 so they don't contribute to the Avg result.

The important thing is that I can enter 1 value on my own to see how Avg will change? And I can change my number as many times as I wish.

For example, if I enter 2000, the Avg value will change to 1290. My entry is 23rd value.

So, is there a way to calculate what I need? Or it's not possible even for the math due to too many unknown variables?

Answer 1

You cannot know. For example, take the sets $\{0,1,6,13\}$ and $\{0,3,4,13\}$ . For both, you have Avg $5$, High $13$, Low $0$

However, in the first, you have the same number of values above and below the average, in the second, you have more numbers below the average.