What is an empirical CDF plot?

An empirical CDF plot is a graph that you can use to evaluate the fit of a distribution to your data, estimate percentiles, and compare different sample distributions. An empirical CDF plot does the following:
  • Plots each unique value vs the percentage of values in the sample that are less than or equal to it, and connects the points with a stepped line.
  • Fits a cumulative distribution function (CDF) for the selected distribution so that you can examine how well the distribution fits your data.
  • Displays a table with the distribution parameter estimates and the number of observations (N) for your data.

If you hold the pointer on a point on the stepped line, Minitab displays the row number and x- and y-values for the point. If you hold the pointer on the fitted line, Minitab displays the estimated percentiles for multiple points.

An empirical CDF plot performs a similar function as a probability plot. However, unlike a probability plot, the empirical CDF plot has scales that are not transformed and the fitted distribution does not form a straight line.

Example of an empirical CDF plot

A manager at a fast food restaurant would like to know the percentage of customers who have to wait the target time of 4 minutes or less for their food. The manager records the wait times for 15 customers and plots them.

This empirical CDF plot reveals the following:
  • The normal distribution seems to fit the sample; therefore, the manager can use the fitted line to estimate percentiles. If it hadn't fit, the manager could try fitting CDF lines for other distributions.
  • The mean wait time is 3.573; the standard deviation is 0.5700.
  • It seems that about 80% of the data fall below 4.0. The manager can hold the pointer on the CDF line to get exact numbers. The manager could also add a percentile line at 4 minutes.

The plot shows observations from only one restaurant. The manager could also display and compare data for several restaurants on the same empirical CDF plot.

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