Make a Box and Whisker Plot
A box and whisker plot is a diagram showing statistical distribution of a data set. This plot makes it easy to see how the data is distributed along a number line. Best of all, a box and whisker plot is easy to make.
Steps
- Gather your data.
Let's say we start the numbers 1, 3, 2, 4, and 5. These will be used for calculation examples. - Organize the data from least to greatest. Take all your numbers and line them up in order, so that the smallest numbers are on the left and the largest numbers are on your right. In our case, the order of the numbers is 1, 2, 3, 4, and 5.
- Find the median of the data set. The median is the middle number in an ordered data set. (This is why we lined up all the numbers in Step 2.) For the data set in our example, 3 is the number that's exactly in the middle, and therefore is our median. The median is also called the second quartile.
- In a data set with an odd amount of numbers, the median will always have the same amount of numbers on either side of it. For the data set 1, 2, 3, 4, 5, the median number, 3, has 2 numbers before it and 2 numbers after it. That's how we can be sure that it's our median.
- What if the data set you're working with has an even amount of numbers? What if you had to find the median of 2, 4, 4, 7, 9, 10, 14, 15? You find the median here by taking the two middle numbers and finding their average. In our example, you would take 7 and 9 — the two middle numbers — add them up and divide them by 2. 7 + 9 equals 16, and 16 divided by 2 equals 8. The median of this data set would be 8.
- Find the first and third quartiles. We've already found the second quartile of the data set, which is our median. Now we need to find the median of the lower half of the data set; in our example it would be the median of the two numbers to the left of 3. The median of 1 and 2 is (1 + 2) / 2 = 1.5. Do the same to find the median of the two numbers to the right of 3. (4 + 5) / 2 = 4.5.
- Draw a plot line. This should be long enough to contain all of your data, plus a little extra on either side. Make sure to place the numbers at even intervals. If you're dealing with decimals, such as 4.5 and 1.5, be sure to label them as well.
- Mark your first, second, and third quartiles on the plot line. Take the values of your first, second, and third quartiles and make a mark at those numbers on the plot line. The mark should be a vertical line at each quartile, starting slightly above the plot line.
- Make a box by drawing horizontal lines connecting the quartiles. Connect the top or the first quartile to the top of the third quartile, going through the second quartile. Connect the bottom of the first quartile to the bottom of the third quartile, making sure to go through the second quartile.
- Mark your outliers. Find the smallest, and then the largest, numbers in your data set and mark them on the plot line. Mark these points with a small dot. In the case of our example, the lower outlier is 1 and the upper outlier is 5.
- Connect your outliers to the box with a horizontal line. The straight line that connects the outliers is informally called the "whiskers" of the box and whiskers plot.
- Finished. Look at a box and whiskers plot to visualize the distribution of numbers in any data set. You can easily see, for example, whether the numbers in the data set bunch more in the upper quartile by looking at the size of the upper box, as well as the size of the upper whisker. Box and whisker plots are great alternatives to bar graphs and histograms.
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