Name______ Reference: Creating Box Plots
When we looked at the median, we learned that understanding the middle number of a data set can help us describe what is typical about a data set. We can also get insight into the distribution of a data set by dividing it into four parts.
Quartiles are the numbers that are the middle of the top and bottom half of data sets.
Box plots, or Box-and-Whisker Plots, are created using the “Five Point Summary”—
the lower extreme (minimum), lower quartile, median, upper quartile, and upper extreme (maximum).
Another way to think of it is in terms of percent--
0% 25% 50% 75% 100%
lower lower median upper upper
extreme quartile quartile extreme
“HOW TO”
Part 1: Identifying the “Five Points”
1. Order the data from least to greatest.
2. Find the median.
* If the data has an even number of values, find the mean of the middle two numbers.
In this case, you will use the higher number to help you calculate the upper quartile.
Use the lower median number to help you calculate the lower quartile.
3. Then, find the median of the lower half of the data. This is your lower quartile.
If there is no middle value in the lower or upper half of the data set, use the mean of the two middle values.
4. Next, find the median of the upper half of the data. This is the upper quartile.
5. Finally, find the lower extreme (minimum) and upper extreme (maximum).
(6). To find the Interquartile range, subtract: Q3 (upper quartile) – Q1 (lower quartile)
This tells you how the range of the middle 50 percent of the data.
Part II: Create Box Plot
6. Draw a number line. Usually you will go up by ones, but the scale may need to change if there is a wide range of data.
7. Plot the 5 points above the number line.
8. Draw vertical lines through the lower quartile, median, and upper quartile.
9. Form a box by connecting the vertical lines from the lower quartile, median, and upper quartile.
10. Finally, draw whiskers (lines) from the extremes to the box.
By finding the middle values of the data set, you have separated the data into four equal groups, called quartiles.
The distance between the points in the box plot tells you about the distribution of the data in the quartiles.
A shorter distance, as in Q1, means the quartile data is bunched together.
A longer distance, as in Q4, means the quartile data is spread out.