Examining Distributions
overview 

Use these graphs to assess and compare properties of distributions, such as:

·    Where sample values are centered.

·    Whether a sample distribution is symmetrical or skewed.

·    Whether sample data follow a specific distribution.

·    How many peaks exist in the sample distribution (more than one peak can indicate that data are from multiple populations).

·    What the most commonly observed values in the sample are.

Graph

Uses

Histogram

 

Use a histogram to evaluate the shape and central tendency of your data, and to assess whether or not your data follow a specific distribution such as the normal distribution.

Bars represent the number of observations falling within consecutive intervals or bins. Because each bar represents many observations, a histogram is most useful when you have a large amount of data.

Display options include fitted distribution and lowess lines.

Dotplot

 

Use a dotplot to evaluate the shape and central tendency of your data. Like a histogram, a dotplot is divided into bins. However, a dotplot can be more useful than a histogram when you have a small amount of data because:

·    By default, a dotplot has many more bins than a histogram.

·    Each dot represents a single observation (or a small number of observations).

Dotplots are also useful for comparing groups of data.

Stem and Leaf

 

Use a stem-and-leaf plot to display the actual data values in a binned format. Though similar to a dotplot, a stem-and-leaf plot:

·    Is turned on its side.

·    Uses the leading digits of the sample values to determine the bins (for example, one bin may have values between 0 and 9, another bin may have values between 10 and 19, and so on).

·    Displays digits from the individual values instead of dots.

·    Is displayed in the Session window, rather than a Graph window.

Probability Plot

 

Use a probability plot to:

·    Determine how well your data follow a specific distribution. The degree of fit is indicated by the degree to which the data points follow the fitted line.

·    Obtain parameter estimates and estimated population percentiles.

·    Compare sample distributions.

Minitab plots the value of each observation against its estimated cumulative probability. The scales are transformed as necessary so that the fitted distribution forms a straight line.

Display options include confidence intervals and percentile lines.

Empirical CDF

 

Use an empirical cdf (cumulative distribution function) graph to:

·    Determine how well your data follow a specific distribution. A good fit is indicated when the stepped function follows the fitted line fairly closely.

·    Obtain parameter estimates and estimated population percentiles.

·    Compare sample distributions.

Minitab plots the value of each observation against its actual cumulative probability. Unlike a probability plot, the scales of an empirical cdf are not transformed and the fitted distribution does not form a straight line.

Display options include percentile lines.

Probability Distribution Plot

Use a probability distribution plot to:

·    View the shape of a distribution.

·    Understand how distribution parameters affect the distribution shape.

·    Teach the concepts of confidence intervals and hypothesis testing.

·    Determine critical values and p-values.

Boxplot

 

Use a boxplot to assess and compare distribution characteristics such as median, range, and symmetry, and to identify outliers.

Display options include symbols for the mean and boxes for the median confidence intervals.