Measures of Center

Algebra 2 · Axiom Academy

Mean, median, and mode — how to find the "center" of a data set, and which one to trust when the data gets messy. The mean (written or ) is the everyday "average": add every value, then divide by how many values there are. Sum the values, then divide by the count n 2. The Median — the Middle Value The median is the middle value once the data is put in order. Sort the numbers, then read off the one in the center. With an even count there is no single middle, so average the two middle values. For the set 2, 4, 6, 8 the two middles are 4 and 6: 3. The Mode — the Most Frequent Value The mode is the value that shows up most often. Stack the data by value and the tallest stack wins — for 3, 5, 7, 7, 8 the value 7 appears twice, so the mode is 7. 3, 3, 5, 7, 7 has two modes — 3 and 7 both appear twice. A set can have several modes. 2, 4, 6, 8 has no mode — every value appears exactly once, so nothing is "most" frequent. 4. Which One Should You Trust? Here is where the choice matters. Start with the tidy, symmetric set 2, 4, 5, 6, 8 — its mean and median are both 5. Now drop in a single outlier , the value 20, and watch what happens. the data is roughly symmetric with no wild outliers, or you need it for further calculation (it uses every value). the data is skewed or has outliers — incomes, home prices, wait times. It reports a truly typical value. You can now build all three measures of center from what they do — and you know which one tells the truth when the data gets messy.

This is the written version of the interactive lesson above. See the full Algebra 2 course.