## Box and Whisker Plots

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-ID.A.1

What are Box and Whisker Plots?
When we plot grouped data on a graph, we have to calculate some basic quantities which help in identifying the trends of the plotted data. The visualization of the data helps in the identification of outliers, the symmetry of the data, how tightly packed the data is if the data is skewed, and which quantities lie in its quartiles.
Some of the common modes of visualizing the data for all the above-mentioned quantities include density plot, histogram, and box-and-whisker plots. The box-and-whisker plot, also known as simply box-plot, is based on five numbers of the data set including upper quartile, lower quartile, median, minimum value, and the maximum value.
Upper Quartile is the value in the data set that lies at the 75th-percentile of the graph and is represented as Q_{1}. Lower Quartile is the value in the data set that lies at the 25th-percentile of the graph and is represented as Q_{3}.
The median of the data set is the middle value of the entire data. If the data set has an even number of values, then the median value is the average of the two values that lie at the center. If the data set has an odd number of values, the median value is the one value that lies in the middle of the data.
Use an equal-interval scale and draw a rectangular box. One end of the rectangular box must lie at Q_{1} and the other end of the box must lie at Q_{3}. The next step is to draw a vertical line at the median value, minimum value, and maximum value.

### Printable Worksheets And Lessons

- Data Set of 9 Step-by-step Lesson- I give you nine simple pieces of data and ask you to generate an entire box and whisker plot for it.
- Guided Lesson - Time to interpret a premade box and whisker plot. Students will determine the median, lower and upper quartiles.
- Guided Lesson Explanation - I explain it and add the visuals too. We get many thankful people emailing about this one.
- Practice Worksheet - I give you a single box and whisker plot and ask you every question I could possible think of. There are a lot of them.
- Matching Worksheet - It is a fun match the value to their label activity. We look at many different measures here.
- Box and Whisker Plots Five Worksheet Pack - Warning! You will need a lot of scrap paper if you plan to do all five worksheets.

#### Homework Sheets

We work on understanding and reading a set box and whisker plot.

- Homework 1 - Find the median (middle number): Median = 1/2 (n + 1), n is the number of data values (9) 1/2 (9 + 1) = 5 or 5th data value.
- Homework 2 - The median is denoted by the middle number of the boxes.
- Homework 3 - The lower quartile is start of the left box and the upper quartile is end of the right box.

#### Practice Worksheets

These sheets were spaced well to be used along with your students.

- Practice 1 - Order the data and find the range.
- Practice 2 - Use the box and whisker plot to answer the questions below.
- Practice 3 - What is the median, lower quartile, and upper quartile?

#### Math Skill Quizzes

Look close at you might find some very unique questions for your students.

- Quiz 1 - A common question for you: What is the minimum value?
- Quiz 2 - What percentage of data is located between the lower quartile and the median?
- Quiz 3 - Draw a box and whisker plot for the data set: 26, 24, 23, 23, 28, 22, 21, 22, 22

### When Would You Want to Display Your Data This Way?

Box and whisker plots are a great way to display large pools of data in a nice a succinct chart. This makes it very helpful to display the scores on examinations of tests that many people have taken. For example, the SAT and ACT data is often displayed this way. This helps the test takers to see where their skills were demonstrated as compared to their peers. This method of displaying results is also helpful for anything that has a great deal of change over time because it tends to almost ignore outliers that other charts seem to give you a general sense of. They are really helpful for understanding a population, but they often neglect to communicate individual trials to any extent at all.