# Boxplot

## Summary

Provides a static picture of the location and spread of the Y variable (the process output) by showing the minimum and maximum values, first quartile (25% of points are less than this value), third quartile (75% of points are less than this value), median (or mean), and potential outliers. If you also include a categorical X variable, you can look at the location and spread of the Y at each level (for example, factor setting) of the X variable.

• What is the general location of the Y data?
• How wide is the spread of the Y data?
• Does the sample contain any unusual data points (outliers)?
• Does changing the level of an input variable (X) affect the location or the spread of the output Y?
When to Use Purpose
Mid-project The first rule in data analysis is to always plot your data before running any statistical tests. The boxplot is a logical choice for comparison tests where you are looking at what happens to the process output under various conditions, such as changes to a process input.
Mid-project Assess if an input (X) has an impact on the process mean or process variation and help eliminate noncritical X's from consideration.
Mid-project Identify levels (settings) of the process input that have the desired impact on the output mean or variation.
Mid-project Communicate the effects of process inputs on the process output to project stakeholders.

### Data

Numeric Y, with optional discrete X (categories for comparison).

## How-To

1. Choose from one of two common data layouts that you can use with boxplots:
1. Choose Boxplot with groups (stacked data) when you enter one column for the Y variable and one for the X (categorical) variable (optional). Note: You can have up to four categorical variables. Minitab draws a separate box for each combination of levels of the categorical variables; however, the boxes all appear in the same graph window. This display is handy for making comparisons across levels of X variables.
2. Choose Boxplot with multiple Y's (unstacked data) when you enter the Y data into a separate column for each level of the X variable. Minitab draws a separate box for each Y. The boxes can be plotted either in separate graph windows or in the same graph window with a common scale.

## Guidelines

• The boxplot is very prone to misinterpretation when the sample size is small. When the sample size is less than 20, use a dotplot or individual value plot.
• The boxplot provides a good visual comparison even when the number of levels of an X variable are high. If the number of levels of an X variable is greater than five, the boxplot provides a better visual comparison than the dotplot (assuming more than 20 points per category).
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