Math 1 · Unit 12 · Lesson 2

Center, the Mean and the Median

Two ways to describe the middle. The mean is the fair-share number, add and divide, the same averaging as the midpoint, and it is the balance point of the dot plot. The median is the middle value in order. One extreme value pulls the mean but leaves the median alone, because the median only cares about the order. So the median is resistant, and skewed data is described with the median.

About 40 minutes The median resists

The big idea

A measure of center is one number for the middle of the data. The mean is the fair-share value, add all the values and divide by how many, the same averaging as the midpoint in Unit 11, and it is the balance point of the dot plot. x-bar names the mean of a sample and mu the mean of a whole population, found the same way. The median is the middle value when the data is in order, or the average of the two middles when the count is even. The two can disagree, and the reason matters: a far-out value pulls the mean toward it, because every value's size goes into the sum, but leaves the median alone, because the median only uses the order. The median is resistant and the mean is not. So the shape picks the center: the mean for roughly symmetric data, the median for skewed data or data with extreme values, like the songs, where the median of 12 describes a typical student better than the mean of about 15.8.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Two ways to find the middleShape, center, and spread, every time. 3The median resistsThat is the key idea. 4Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the mean as the balance point, x-bar and mu, the median, the class periods before and after, and the shape-picks-the-center rule. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Pictures of Data and Their ShapesThe tail tells you the name. Next lesson: Spread, the IQR and the Standard DeviationHow spread out is it? The IQR and the standard deviation. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.S-ID.2 (compare center with median and mean), NC.M1.S-ID.3 (the effect of extreme values on center).