The range chart always checks for consistency within the subgroups. In this case, the variation within the subgroups is the daytoday variation. Thus, the range chart will check to see if all 46 individuals show the same amount of variation when they perform the same task repeatedly. If a person should have a range value that is above the limit on the range chart, then that person could be said to have detectably greater variation in the way he performs the skills test. No ranges fall above the limit of 14.3, so we may conclude that all 46 men show the same amount of daytoday variation in performing this task. The average chart always looks for differences between the subgroups. In this case, when we go from subgroup to subgroup, we are changing persons. Thus, the persontoperson differences will show up on the average chart. Because it is the average range that is used to compute the limits for both charts, the limits will reflect the uncertainty due to the natural human variation in performing this task. Thus, the limits on the average chart define that amount of variation in the average scores which can be attributed to the natural variation inherent in performing this task repeatedly. In order for one person to be said to be detectably above average  or detectably below average  in his proficiency at this task, he will have to have an average that is outside the control limits on the average chart. Those with averages that fall within the limits must be said to be indistinguishable from each other. Fortyfive of the individuals have averages that fall within the limits of 68.2 to 77.3. One man, with an average of 67.5, shows a detectably different level of proficiency. His different level of proficiency cannot be explained by the normal, daytoday variation that covers all the other persontoperson differences. Now that you know what these data are telling you, it is time for the rest of the story  these data are the scores for the 1997 Master's Tournament. You can get the data from the golf portion of the sports section of any newspaper for April 14  but then you probably already know who was detectably different from all the rest. Can you see how the average chart tells you why par is 72? And can you express in words what the average range of 6.26 represents? The answers to these two questions will help you learn how to use Shewhart's charts more effectively. About the author Donald J. Wheeler is an internationally known consulting statistician and the author of Understanding Variation: The Key to Managing Chaos and Understanding Statistical Process Control, Second Edition. © 1997 SPC Press Inc. Telephone (423) 5845005 or email dwheeler @qualitydigest.com. 

