He purpose of an x-bar chart is to determine whether there has been a: change in the AOQ. change in the number of defects in a sample. change in the percent defective in a sample. change in the dispersion of the process output. change in the central tendency of the process output.

The change in the central tendency of the process output.

Step-by-step explanation:

Lets examine each of the listed options

The change in the percent defective in a sample is associated with the change in average outgoing quality (AOQ).

The change in the dispersion of the process output is associated with R-chart since the function of R-chart is to detect changes in the dispersion.

The change in the number of defects in a sample is associated with C-chart since the function of a C-chart is to show the number of flaws per unit in a sample.

The change in the central tendency of the process output is associated with X-bar chart since the function of X-bar chart is to check whether the values are within the appropriate limits (central tendency) of the process output or not.

Therefore, the purpose of an X-bar chart is to determine whether there has been a change in the central tendency of the process output.