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Creating & Interpreting Box Plots: Process & Examples

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  • 0:02 Observing and Analyzing Data
  • 0:46 Analyzing a Box Plot
  • 2:58 Creating a Box Plot
  • 5:06 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Box plots are an essential tool in statistical analysis. This lesson will help you create a box plot and understand its meaning. When you are finished, test your understanding with a short quiz!

Observing and Analyzing Data

Isabel is a news director at a local television station. She just hired two new anchors for her noon newscast. Two weeks later, Isabel's boss wants to meet with her about the new anchors. He's not sure if the audience likes the change. Isabel conducts a survey of a random group of 15 people, asking them to rank the anchors on a scale of 1 to 10, with 10 being the best and 1 being the worst. These are the ranks she got back on the survey:

3, 3, 7, 8, 7, 4, 4, 10, 1, 5, 1, 7, 2, 7, 9

Isabel now needs to analyze this data. She can use a box plot to visualize the data.

Analyzing a Box Plot

A box plot is a graphical representation of the distribution in a data set using quartiles, minimum and maximum values on a number line.

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This is an example of a box plot. To understand the different elements of a box plot, you need to understand quartiles, interquartile range and median.

A quartile is a group of values and/or means that divide a data set into quarters, or groups of four. Do not be confused here; a quartile is a value, not a group of numbers. Think of a quartile as a 'cut-off point' for each group. A group has to start and stop somewhere, and that's exactly what a quartile does.

The interquartile range is a value that is the difference between the upper quartile value and the lower quartile value.

The median is the midpoint value of a data set, where the values are arranged in ascending or descending order.

For more information about quartiles, check out our chapter on summarizing data.

First, let's look at some of the pieces and parts of a box plot. Take a look at this example.

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The first thing you may notice is the purple box on the right side of the graph sitting directly above the number line. This box represents the interquartile range. The line that creates the left side of the box represents lower quartile, or quartile 1, and the line that creates the right side of the box represents the upper quartile, or quartile 3.

The line in the middle of the box, slightly to the left, is the median. The vertical line on the far left is the extreme minimum value, and the vertical line on the far right is the extreme maximum value. These are the smallest and the largest numbers in the data set. Finally, the line that extends horizontally from the extreme minimum to the extreme maximum represents the range of the data set.

You may also notice that the extreme minimum is pretty far away from the box, and the box is located farther to the right. This means that the data is partially skewed and that the extreme minimum is an outlier.

Creating a Box Plot

Let's take another look at Isabel's data set:

3, 3, 7, 8, 7, 4, 4, 10, 1, 5, 1, 7, 2, 7, 9

To create a box plot, we need to find the quartiles and the minimum and maximum values. First, we need to order the data from least to greatest, like this:

1, 1, 2, 3, 3, 4, 4, 5, 7, 7, 7, 7, 8, 9, 10

Just by looking at this order, we can see that our extreme minimum, or our minimum value, is 1 and our extreme maximum, or our maximum value, is 10.

Now we need to find the median of this data set. Our median value is 5.

Now we need to find quartile 1 and quartile 3. Our first quartile is 3. Our third quartile is 7. Now we can use all of these points and plot them on our number line.

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