Use graphs to explore data and assess relationships between the variables. Also, use graphs to summarize data and to help interpret statistical results.

## Boxplot

Use a boxplot to assess and compare the shape, central tendency, and variability of sample distributions, and to look for outliers.

A boxplot works best when the sample size is at least 20. For example, a scientist creates a boxplot to compare the height of plants grown with two different fertilizers and a control group with no fertilizer. To see an example, go to Minitab Help: Example of Boxplot.

### Data considerations

Your data must be a numeric value for Y, with an optional discrete value for X (categories for comparison). A boxplot works best when the sample size is at least 20. If the sample size is too small, the quartiles and outliers shown by the boxplot may not be meaningful. For details, go to Minitab Help: Data considerations for Boxplot.

## Contour plot

Use a contour plot to examine the relationship between a response variable and two predictor variables.

In a contour plot, the values for two predictor variables are represented on the x- and y-axes, and the values for the response variable are represented by shaded regions, called contours. A contour plot is like a topographical map in which x-, y-, and z-values are plotted instead of longitude, latitude, and altitude.

A food scientist wants to determine the optimal time and temperature for heating a frozen dinner. The scientist prepares 14 samples at various times and temperatures, and then has professional food tasters rate each sample for overall quality. The scientist creates a contour plot to examine the results. To see an example, go to Minitab Help: Example of Contour Plot.

### Data considerations

If possible, the x- and y-values should be spaced regularly to form a grid. Usually, the z value is the response that you want to explain or predict and the x and y values are the explanatory variables. For details, go to Minitab Help: Data considerations for Contour Plot.

## Dotplot

Use a dotplot to assess and compare sample data distributions.

A dotplot divides sample values into small intervals and represents each value or small group of values with a dot along a number line. A dotplot works best when the sample size is less than approximately 50.

For example, a quality engineer creates a dotplot to examine the distribution of the amount of torque that is required to remove the caps from a sample of shampoo bottles. To see an example, go to Minitab Help: Example of Dotplot.

### Data considerations

Your data must be numeric values for Y, with optional discrete values for X (categories for comparison). A dotplot works best when the sample size is less than approximately 50. If the sample size is 50 or greater, a dot may represent more than one observation. Consider using a boxplot or a histogram in addition to the dotplot so that you can more easily identify primary characteristics of the distribution. For details, go to Minitab Help: Data considerations for Dotplot.

## Histogram

Use a histogram to examine the shape and spread of your data.

A histogram divides sample values into many intervals and represents the frequency of data values in each interval with a bar. A histogram works best when the sample size is at least 20. However, a sample size that is considerably greater than 20 may better represent the distribution.

For example, a quality engineer creates a histogram to examine the distribution of the amount of torque that is required to remove the caps from a sample of shampoo bottles. To see an example, go to Minitab Help: Example of Histogram.

### Data considerations

Your data must be numeric values for Y and X. A histogram works best when the sample size is at least 20. If the sample size is too small, each bar on the histogram may not contain enough data points to accurately show the distribution of the data. If the sample size is less than 20, consider using an individual value plot instead. For details, go to Minitab Help: Data considerations for Histogram.

## Individual value plot

Use an individual value plot to assess and compare sample data distributions.

An individual value plot shows a dot for the actual value of each observation in a group, making it easy to spot outliers and see distribution spread. An individual value plot works best when the sample size is less than approximately 50.

Like a boxplot, an individual value plot helps you to identify possible outliers and visualize the distribution of your data. However, unlike a boxplot, an individual value plot displays each value separately. Separate values are especially useful when you have relatively few observations or when it is important to assess the effect of each observation.

For example, an engineer creates an individual value plot to compare the elasticity of plastic samples made with different additives. To see an example, go to Minitab Help: Example of an individual value plot of multiple Y variables.

### Data considerations

Your data must be a numeric Y variable, with an optional discrete X variable (categories for comparison). An individual value plot works best when the sample size is less than approximately 50. If the sample is too large, the data points on the plot may be too densely packed together and the distribution may be difficult to assess. If the sample size is greater than 50, consider using a boxplot or a histogram instead. For details, go to Minitab Help: Data considerations for Individual Value Plot.

## Interactions plot

Use an interactions plot to show how the relationship between one categorical factor and a continuous response depends on the value of the second categorical factor. This plot displays means for the levels of one factor on the x-axis and a separate line for each level of another factor.

For example, researchers at the department of highway safety want to understand the relationship between driver experience and road type on the number of steering corrections. The researchers create an interaction plot to display the effect of the factors on each other and on the response. To see an example, go to Minitab Help: Example of Interaction Plot.

### Data considerations

The response variable (Y) should be continuous. The data should include one or two categorical factors (X). For details, go to Minitab Help: Data considerations for Interaction Plot.

## Main effects plot

Use a main effects plot to see how one or more categorical factors influence the continuous response.

For example, a carpet manufacturer wants to see the results for a one-way ANOVA. The manufacturer creates a main effects plot of the average carpet durability scores by carpet type. To see an example, go to Minitab Help: Example of Main Effects Plot.

### Data considerations

The response variable (Y) should be continuous. The data should include one or two categorical factors (X). For details, go to Minitab Help: Data considerations for Main Effects Plot.

## Matrix plot

Use a matrix plot to assess the relationships between several pairs of variables at once. A matrix plot is an array of scatterplots.

For example, a business analyst wants to study successful small-to-medium size manufacturing companies. The analyst collects data on the number of clients, rate of return, sales, and the years the companies have been in business. As part of the initial investigation, the analyst creates a matrix plot to examine the relationships between number of clients, rate of return, and years. To see an example, go to Minitab Help: Example of Matrix Plot.

### Data considerations

Although there are no formal guidelines for the amount of data needed for a scatterplot, larger samples more clearly indicate patterns in the data. A scatterplot that has a fitted regression line is most effective when the sample size is approximately 40 or greater. If the sample size is less than 40, the fitted regression line may not be as accurate. You should consider the sample size for each scatterplot in the matrix plot. For details, go to Minitab Help: Data considerations for Matrix Plot.

## Multi-vari chart

Use a multi-vari chart as a preliminary tool to investigate variation in your data, including cyclical variations and interactions between factors.

A multi-vari chart provides a graphical representation of the relationships between factors and a response. The multi-vari chart displays the means at each factor level for every factor. In Minitab, each multi-vari chart can display up to four factors.

For example, a manufacturer produces plastic pipes using two different machines with three temperature settings. The quality engineer is concerned about the consistency of pipe diameters from the different machines and settings. The engineer creates a multi-vari chart to investigate the variation in pipe diameters. To see an example, go to Minitab Help: Example of Multi-Vari Chart.

### Data considerations

To calculate the mean response at different factor levels, the multi-vari chart requires numeric response data. You may have up to four numeric, text, or date/time factors. Each factor must have at least 2 levels. For details, go to Minitab Help: Data considerations for Multi-Vari Chart.

## Scatterplot

Use a scatterplot to investigate the relationship between a pair of continuous variables. A scatterplot displays ordered pairs of X and Y variables in a coordinate plane.

For example, a medical researcher creates a scatterplot to show the positive relationship between Body Mass Index (BMI) and body fat percentage in adolescent girls. To see an example, go to Minitab Help: Example of Scatterplot.

### Data considerations

The data must include one or more pairs of columns of numeric or date/time data. For details, go to Minitab Help: Data considerations for Scatterplot.

## Surface plot

Use a surface plot to examine the relationship between a response variable (Z) and two predictor variables (X and Y), by viewing a three-dimensional surface of the predicted response. You can choose to represent the predicted response as a smooth surface or a wireframe.

For example, a food scientist wants to determine the optimal time and temperature for heating a frozen dinner. The scientist prepares 14 samples at various times and temperatures, and then has professional food tasters rate each sample for overall quality. The scientist creates a 3D surface plot to examine the results. To see an example, go to Minitab Help: Example of 3D Surface Plot.

### Data considerations

If possible, the x- and y-values should be spaced regularly to form a grid. For details, go to Minitab Help: Data considerations for 3D Surface Plot.

## Time series plot

Use a time series plot to look for patterns in your data over time, such as trends or seasonal patterns. A time series plot can help you choose a time series analysis to model your data.

For example, a stock broker compares the monthly performance of two stocks during the past two years. The stock broker creates a time series plot to visualize the performance of the two stocks. To see an example, go to Minitab Help: Example of Time Series Plot.

### Data considerations

Record data in chronological order. Time series data are collected at regular intervals and are recorded in time order. You should record the data in the worksheet in the same order that you collect it. If the data are not in chronological order, you cannot use a time series plot to assess time-related patterns in the data. Time series plots assume that data are collected at regular intervals, such as once a day, or once a month. If you collect data at irregular intervals, then a time series plot may be misleading. For details, go to Minitab Help: Data considerations for Time Series Plot.