### Discrete and Continuous Data

A clear understanding of the difference between discrete and continuous data is critical to the success of any Six Sigma practitioner.  The decision about which statistical test is appropriate under a specific set of circumstances very often depends on whether the underlying data is discrete or continuous.

Discrete data are also referred to as attribute data.  Discrete data take on a finite number of pre-determined points.  The values that discrete data can take on are restricted to a list of two or more possibilities.

Discrete data may be binary, where the value fits into one of two categories.  For example, the sex of a person can take on two predetermined values – male or female.   A product may be defective or not defective.

Discrete data may be ordinal, where values fit into one of three or more categories and there is an order or rank to the values.  For example, the length of a gentleman’s suit coat may fall into one of three categories – short, regular or long.

Finally, discrete data may be nominal where the data fit into one of three or more categories where the order of the categories is arbitrary.  For example, the color of a new car might fall into one of five categories – red, blue, silver, white and black.

It should be noted that count data is discrete data.   Items are counted in discrete units – one unit, two units, three units, etc.  For example, the number of correct answers on a 25 question test could be one of 26 values ranging from zero to 25.

Continuous data are also referred to as variable data.  Continuous data exist on an interval and can take on any value.  The number of possibilities for a continuous measurement within an interval is infinite.  Therefore, continuous data are measured on an infinitely divisible continuum.

Examples of continuous data are the Ph of a solution, the length of an item in inches, and the weight of an item in pounds.  A good rule of thumb is that if the unit of measure can be divided in half and still make sense, the data is continuous.

A special case, and one which often confuses Six Sigma students, is percentage data.  Technically speaking, percentage data is discrete because the underlying data that the percentages are calculated from is discrete.  For example, the percentage of defects is calculated by dividing the number of defects (discrete count data) by the total number of opportunities to have a defect (discrete count data).  In practice, percentage data are often treated as continuous because the percentage can take on any value along the continuum from zero to 100%.  In addition, dividing a percentage point into two or more parts still makes sense.

Discrete data are easy to collect and interpret.  In Six Sigma we often talk about the number of defects, or the number of defects per million opportunities (DPMO) which are both discrete data.    The downside of discrete data is the loss of precision in measurement and the need for a larger amount of data to uncover patterns.

Continuous data give a greater sense of the variation that is present.  For example, consider someone who has been determined to have been speeding on a highway where the speed limit is 65 miles per hour.  If we use discrete data, we only know whether someone was speeding (over the speed limit of 65 mph) or not speeding (at or under the speed limit of 65 mph).  If we collect continuous data we have more information to work with.  For example, knowing that someone was traveling 68 miles per hour gives us a different understanding of their speed than knowing that they were traveling 95 miles per hour, even though both would be classified as speeding using discrete data.

In practice it is recommended to collect continuous data whenever possible and practical, and then convert it to discrete as required using a threshold value.  In the case of highway speed, we would collect continuous data (how fast the automobile was traveling in miles per hour) and then determine whether the result is speeding or not speeding by comparing the actual speed to the threshold value of 65 miles per hour (the speed limit).