Solution:

Variables control charts are used to evaluate variation in a process where the measurement is a variable–i.e. the variable can be measured on a continuous scale (e.g. height, weight, length, concentration). There are two main types of variables control charts. One (e.g. x-bar chart, Delta chart) evaluates variation between samples. Non-random patterns (signals) in the data on these charts would indicate a possible change in central tendency from one sampling period to the next. One way of thinking about the use of a variables control chart is that you are testing the hypothesis that a particular sample mean came from the population of sample means represented by the control limits of the process. If the particular sample mean is within the control limits, your concusion is that it does come from that population. If the particular sample mean is outside the control limits, you conclusion is that it may have come from some other distribution (i.e. a distribution with a mean that is higher or lower than this population mean. [NOTE: There are other signals that may indicate an out-of-control signal that will be discussed in the Lesson Six Presentation.]

The other type of variables control chart (e.g. R-chart, S-chart, Moving Range chart) evaluates variation within samples. Non-random patterns (signals) in the data on these charts would indicate a possible change in the variation within the samples.