Mean, Median, Mode

Pre-Algebra · Axiom Academy

Three ways to name the "center" of a data set — and why they can disagree. Our running example: seven friends report how many books they read last month. 1. The Mean — the balance point The mean (the everyday "average") adds up every value and splits the total evenly across all of them. Geometrically it is the balance point of the data: lay the values on a number line and the mean is where they would balance, because the gaps on the left exactly cancel the gaps on the right. sum every value, then divide by how many there are The other two centers ignore the arithmetic and look at position and frequency instead. The median is the value sitting in the middle once the data is in order. The mode is simply the value that shows up most often — the tallest stack. In order, the seven values are 3, 3, 3, 4, 6, 7, 9. The middle one (the 4th of 7) is the median = 4 . The value 3 appears three times — more than any other — so the mode = 3 . Notice the mode and the median already disagree. 3. What an Outlier Does to Each Now suppose the friend who read 9 books actually read 30 — a value far from the rest, an outlier . The data is otherwise unchanged. Watch which centers move and which stay put. the mean jumps from 5 to 8 — dragged by the single 30

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