How to Create a Box-and-Whisker Plot: A Step-by-Step Guide
A box-and-whisker plot, also known as a box plot, is a graphical representation of a dataset that displays the distribution of data based on a five-number summary. Here’s a comprehensive guide on how to create and interpret a box-and-whisker plot, both manually and using a calculator.
Step 1: Order the Dataset
To begin, ensure that your dataset is ordered from the least to the greatest value. This step is crucial for accurately identifying the minimum, maximum, and quartiles[4].
Step 2: Identify Key Values
Minimum Value: The smallest value in the dataset.
Maximum Value: The largest value in the dataset.
Median (Q2): The middle value of the dataset when it is ordered. If the dataset has an even number of entries, the median is the average of the two middle values.
First Quartile (Q1): The median of the lower half of the dataset.
Third Quartile (Q3): The median of the upper half of the dataset[4].
Step 3: Calculate Quartiles
For an odd number of entries, the first quartile is the median of the entries up to and including the middle value of the lower half. For an even number, it is the average of the two middle values of the lower half.
Similarly, the third quartile is the median of the entries from the middle value of the upper half to the end. For an even number, it is the average of the two middle values of the upper half[4].
Step 4: Draw the Box Plot
The Box
Mark the first and third quartiles (Q1 and Q3) on a number line.
Draw a rectangle (the box) with its sides corresponding to these quartiles.
Inside the box, draw a line to represent the median (Q2)[4].
The Whiskers
Draw lines (whiskers) from Q1 to the minimum value and from Q3 to the maximum value. These lines should be parallel to the quartile lines.
Connect the whiskers to the box at the points corresponding to Q1 and Q3[4].
Using a TI-83/84 Calculator to Create a Box Plot
If you prefer to use a graphing calculator, here are the steps for a TI-83 or TI-84:
Enter the Data
Press STAT and then 1:Edit to enter the data into list L1. Clear any existing data by arrowing up to L1, pressing CLEAR, and then pressing ENTER[2][3][5].
Calculate Summary Statistics
Press STAT and arrow to CALC. Select 1:1-VarStats and enter L1. Press ENTER to view the summary statistics, including the minimum, maximum, and quartiles[2][3][5].
Graph the Box Plot
Press 2nd and then STAT PLOT. Select 1:Plot 1 and press ENTER to turn on the stat plot.
Use the right arrow key to select the box plot (the fourth graph type) and press ENTER.
Ensure that Xlist is set to L1 and Freq is set to 1.
Press GRAPH to see the box plot. You can adjust the window settings by pressing ZOOM and selecting 9:ZoomStat[2][3][5].
Important Facts About Box-and-Whisker Plots
Five-Number Summary: A box plot is based on the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value[1][2][4].
Scaled Number Line: It is essential to start with a scaled number line to ensure the box plot is useful[1][2].
Quartiles: Q1 is the median of the lower half, and Q3 is the median of the upper half of the dataset[4].
Whiskers: Extend from Q1 to the minimum value and from Q3 to the maximum value[1][2][4].
Calculator Use: TI-83 and TI-84 calculators can automate the process of calculating summary statistics and graphing the box plot[2][3][5].
Interpretation: The box plot helps in visualizing the distribution of data, identifying outliers, and comparing datasets[4].
By following these steps, you can effectively create and interpret box-and-whisker plots, whether manually or using a graphing calculator. This tool is invaluable for understanding and analyzing datasets in various statistical contexts.
