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In this lesson, students learn that they can further decompose a data set into four equal groups and use the quartiles to describe a distribution. They learn that the three quartiles along with the maximum and minimum values of the data set make up a five-number summary.
Students also explore the range and interquartile range (IQR) of a distribution as two ways to measure its spread. Students reason abstractly and quantitatively (MP2) as they find and interpret the IQR as describing the distribution of the middle half of the data.
Let's look at other measures for describing distributions.
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Quartiles are the numbers that divide a data set into four sections. Each section has the same number of data values.
In this data set, the first quartile (Q1) is 30. The second quartile (Q2) is the median, 43. The third quartile (Q3) is 50.
| 22 | 29 | 30 | 31 | 32 | 43 | 44 | 45 | 50 | 50 | 59 |
| Q1 | Q2 | Q3 |
The range is the distance between the smallest and largest values in a data set.
In the data set 3, 5, 6, 8, 11, 12, the range is 9, because .