mean score Or average score?

As your example shows, it depends. A 'mean' number is the one found in the middle (or closest to the middle) of a series of numbers when they are arranged in order of value. So in 6, 8, and 10, the mean number is 8. In 36, 175, 58, 0, 102, and 212, the mean number is 102.
But 'average' requires an equation - add up all the numbers in your series of numbers, and then divide by the number of numbers in your series. 36+175+58+0+102+212=583 and 583 divided by 6 = 97. But as in your example, 6+8+10=24, and 24 divided by 3 = 8.
The average can be higher or lower than the mean, or,as in your case, the same.

Actually Eos, the mean is the arithmetical average, so it IS a calculated value. Your definition applies to the term "median".

oristarA: Both words would be acceptable, although "average" would likely be the word more commonly used in every day English conversation.

I would also amend your sentence as follows:

So the mean score of students A, B and C is 8.

or

So the average score of students A, B and C is 8.

Thanks you both.

Now the question is clear for me.

You're welcome oristarA.