## Order a Set of Data to Find the Median, Quartiles and Extremes

Today’s lesson focuses on data once again. This time, we will be building box-and-whisker plots. To understand a box-and-whisker plot there is some vocabulary to learn first. Our first key word when working with box-and-whisker plots is median.

When working with data, we often have series of numbers that tell us important information. Here is data set showing the number of hours that the average teenager works in a part time job.

16, 10, 8, 8, 11, 11, 12, 15, 10, 20, 6, 16, 8

To work with this set of data, the first thing that we need to do is to order the data. To order means that we write the data in order from least to greatest including any repeated numbers.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20

Next, we find the median. Remember that the median is the middle number in a set of data. Here there are 13 values. The median is 11.

The median is 11.

The next key term that we need to understand is a quartile. A quartile divides the data set into four parts. With the median, our data set is divided into two parts. The first part is the first half up to 10 and the second half starts at 11 and goes to 20. The median is in purple.

Take a look.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20

To use quartiles, we need to divide this data set into four sections not two. To do this, we find the median of the first half of the data and the median of the second half of the data. The median of the first half of the data is called the lower quartile. The median of the second half of the data is called the upper quartile.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20

Here the median is in red.

The lower quartile is the average between 8 and 8. The lower quartile is 8.

The upper quartile is the average between 15 and 16. The lower quartile is 15.5.

The next term that we need to know is the extremes. The term extreme refers to the lowest value in a data set, the lower extreme and the highest value in a data set the upper extreme.

In the set we just looked at, 6 is the lower extreme and 20 is the upper extreme.