Math 1 · Unit 12 · Lesson 2 · part 2 of 4

Two ways to find the middle

Shape, center, and spread, every time.

Two ways to find the middle

Shape, center, and spread, every time. Lesson 1 was shape. This lesson is center: one number that describes the middle of the data, a measure of center. There are two, and they can disagree.

The mean, also called the average

The fair-share number: add all the values and divide by how many. It is the same averaging you used for the midpoint in Unit 11, with more than two numbers.

For 2, 4, 6, 8, 10: 2 + 4 + 6 + 8 + 105 = 305 = 6.

The symbols

x̄, said "x-bar", is the mean of a sample, a part of a bigger group. μ, the Greek letter mu, said "mew", is the mean of a whole population, the entire group. They are found exactly the same way: add and divide. The symbol only says which group the data came from.

The median

The middle value when the data is in order. If the count is even, there are two middle values: average them.

For 2, 4, 6, 8, 10: the middle is 6. For 2, 4, 6, 8: the two middles are 4 and 6, so the median is 5.

The mean is the balance pointPicture the dot plot as a board with the dots as weights. The mean is the spot where the board balances on your finger. A dot far out on one side pulls the balance point toward it, the way a child far out on a seesaw tips it. The median does not care how far out that dot is, only that it is on one side.

Eleven middle schools reported the length of a class period, in minutes: 45, 50, 50, 55, 55, 60, 60, 60, 65, 70, 70. The mean is about 58.2 and the median is 60. Now slide the last value out to 100 minutes, Cherry Lane Middle's extra-long period, and watch.

With the 100 minute period added, the mean jumps to about 61.7, but the median stays at 60. One extreme value moved the mean and left the median alone.

Where to go next

Next: The median resistsThat is the key idea. All the partsCenter, the Mean and the Median