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 then investigate whether the mean or the median is a more appropriate measure of the center of a distribution in a given context. They learn that when the distribution is symmetrical, the mean and median have similar values. When a distribution is not symmetrical, however, the mean is often greatly influenced by values that are far from the majority of the data points (even if there is only one unusual value). In this case, the median may be a better choice.
- 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.
- Explain (orally) that the median is a better estimate of a typical value than the mean for distributions that are not symmetric or contain values far from the center.
- Generalize how the shape of the distribution affects the mean and median of a data set.
- I can determine when the mean or the median is more appropriate to describe the center of data.
- I can find the median for a set of data.
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 \(14 \div 2 = 7\).
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