Discrete and Continuous Data – Recognizing the Difference

The choice of which statistical test to use is often determined in part by whether the data is continuous or discrete.  Our Green Belt course includes an exercise where students are asked to convert continuous data into discrete categories.  For example, time to complete a transaction is continuous data.  Discrete categories for delivering a package might be acceptable for a delivery made in 48 hours or less and unacceptable for a delivery that takes more than 48 hours.  A high percentage of students struggle to complete this exercise correctly because they identify data as continuous when it is discrete.  Continuous data can take on any value, while discrete data has only a finite number of possible values.

Here is a recent example where a student mistakenly identified discrete data as continuous.   The APGAR score is a test given to newborns soon after birth. This test checks five discrete categories – a baby’s Appearance (skin color), Pulse (heart rate), Grimace (reflexes), Activity (muscle tone), and Respiration (breathing) – to see if extra medical care or emergency care is needed. The test is usually given twice: once at one minute after birth, and again at five minutes after birth.

One of three discrete situations is observed and scored in each of the five categories.  For example, the three possible observations for the category breathing are:  not breathing (score as 0), slow or irregular breathing (score as 1) or cries well (score as 2).  The same procedure is used to observe and score heart rate, muscle tone, reflexes and skin color.   As a result, each of the five categories either scores 0, 1 or 2. 

The total APGAR score is the sum of the five individual category scores.  The total AGPAR score therefore is one of the following discrete integer numbers:   0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10.

In her submission the student incorrectly identified the APGAR score as continuous data.  The APGAR score is discrete data because it can only take on a finite set of values.  For APGAR to be a continuous variable, each of the individual scores would need to be able to take on any value between 0 and 2.  For example, breathing effort could be scored as a .68 or as a 1.45 or any other number between zero and 2.  And so on.  That would mean that any value between zero and ten would be possible for the overall APGAR score.

Your comments or questions about this article are welcome, as are suggestions for future articles.  Feel free to contact me by email at roger@keyperformance.com.

About the author:  Mr. Roger C. Ellis is an industrial engineer by training and profession.  He is a Six Sigma Master Black Belt with over 50 years of business experience in a wide range of fields.  Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC.   For a more detailed biography, please refer to www.keyperformance.com