Averages, Explained: The Math Behind Mean, Median, Mode & Weighted Averages
Every calculator that averages numbers runs the same three lines of math: add the values, count them, divide. The mean, the median, the mode, and the weighted average are four different answers to one question β "what is typical here?" β and building a calculator that gets them right means understanding exactly where each one breaks. Here is the math, with worked examples you can check by hand.
The Mean: Add, Count, Divide
The arithmetic mean is the sum of the values divided by how many there are. For test scores 78, 85, 85, 90, 92: the sum is 430, the count is 5, and 430 Γ· 5 = 86 . That is the whole algorithm β and the full guide on how to calculate average walks through it step by step, including decimals and the two-number shortcut (the average of 40 and 60 is 50, exactly halfway between them).
One invariant every implementation should test: the mean always lies between the smallest and largest value.β¦
