Kōkiri Learn

Background reading · Mathematics and Statistics

Mean, median or mode: which average tells the truth?

Three kinds of average, and why the one you choose can change the story.

An average is one number that stands for a whole set of data. There are three common kinds, and they don't always agree.

The three averages

  • Mean: add all the values and divide by how many there are.
  • Median: put the values in order and take the middle one (or halfway between the two middle ones).
  • Mode: the value that appears most often.

    • The range (largest minus smallest) tells you how spread out the data is.

    When they disagree

    Imagine five students' weekly pocket money: $5, $5, $10, $10 and $120. The mean is $30, but four of the five students get far less than that. The median, $10, tells the story better. The $120 is an outlier, a value far from the rest, and it pulls the mean up.

    Choosing

    Use the median when there are outliers or the data is lopsided. Use the mean when the data is fairly even. Use the mode for categories, like the most common way to get to school.

    Be honest about your data

    Before you trust an average, check the data for mistakes, ask whether the sample was fair, and always show the graph as well as the number.

    Sources and further reading

    Written for Kōkiri Learn students in our own words. Check facts against the sources.

    Used in: What the Data Shows