In this lesson, students consider another measure of center, the median, which divides the data into two groups with half of the data greater and half of the data less than the median. To find the median, they learn that the data are to be arranged in order, from least to greatest. They make use of the structure of the data set (MP7) to see that the median partitions the data into two halves: one half of the values in the data set has that value or smaller values, and the other half has that value or larger. Students learn how to find the median for data sets with both even and odd number of values.
Students engage in MP2 as they find the median of a numerical data set and interpret it in context. They begin to see that, just like the mean, the median can be used to describe what is typical in a distribution, but that it is interpreted differently than is the mean.
- Comprehend that the “median” is another measure of center, which uses the middle of all the values in an ordered list to summarize the data.
- Identify and interpret the median of a data set given in a table or on a dot plot.
- Informally estimate the center of a data set and then compare (orally and in writing) the mean and median with this estimate.
Let's explore the median of a data set and what it tells us.
For the Finding the Middle activity, each student will need an index card.
- I can find the median for a set of data.
- I can say what the median represents and what it tells us in a given context.
The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.
For the data set 7, 9, 12, 13, 14, the median is 12.
For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14 \div 2 = 7\).