Mean
A list of numbers is all different. Is there one number that can speak for the whole list, and what does it really mean?
Where you are 3 inside
What this area is about
The mean is the number you get by adding the values and dividing by how many there are. For 4, 5, 5, 8 and 13 it is 35 \div 5 = 7. That one calculation has two meanings, and each one explains something the other does not: it is a fair share, and it is a balance point.
How these fit together
Two definitions, one number. Mean as fair share pools the total and shares it out evenly, which is where the “add up, then divide” rule comes from. Mean as balance point places the values on a number line and finds where the distances above and below cancel, which shows how the mean moves when one value changes.
A procedure. Mean from a frequency table finds the mean when each value comes with a count, and extends the idea to a weighted mean where some values count for more than others.
A path through it
Fair share first, then balance point, then the frequency table. The two meanings can be read in either order, but the computing rule is easiest to meet as a fair share.
The mean is the center that mean absolute deviation measures spread around, and later the average value of a function is the same fair share taken over a continuous interval.