Mean, Median, Mode

Algebra 1 · Axiom Academy

Three ways to find the center of a dataset — seen as the motion that defines each one. 1. The Mean Is the Balance Point The mean is the sum of the values divided by how many there are. But there's a more physical picture: drop each value as an equal weight on a number line, and the mean is the single spot where the line would balance on a fulcrum — the pulls from the left and the pulls from the right cancel out exactly. Sum the values, divide by the count Find the mean of 3, 5, 7, 9, 11 . Watch where the fulcrum settles, then read off the arithmetic. 2. The Median Is the Middle of the Order The median is the value sitting in the middle once the data is sorted. A clean way to find it: order the list, then cross off the outermost pair — the smallest and the largest cancel each other — and keep collapsing inward. Whatever survives in the center is the median. Arrange the values from smallest to largest. Pair off the lowest with the highest, working toward the center. One value is left standing — that's the median. Two survive — average the two middle values. Find the median of 8, 3, 11, 5, 9 . The animation sorts them, then collapses the ends inward. 3. The Mode Is the Tallest Stack The mode is the value that appears most often. Picture stacking a block for each time a value shows up: the value whose stack grows tallest is the mode. A dataset can have one mode, several tied modes, or none at all if nothing repeats.

This is the written version of the interactive lesson above. See the full Algebra 1 course.