Which statement correctly describes what X-bar and R charts monitor in subgroup data?

Which statement correctly describes what X-bar and R charts monitor in subgroup data?

• A. X-bar monitors the mean; R monitors the subgroup mean.
• B. X-bar monitors the median; R monitors the range.
• C. X-bar monitors the mean; R monitors the subgroup range.
• D. X-bar monitors the variance; R monitors the median.

Answer: (C)

In this type of control-chart approach, you’re looking at how a process behaves within small subgroups over time. The X-bar chart tracks the mean of each subgroup, so a drift or shift in the plotted points tells you the process center (the average level) may have changed. The R chart, on the other hand, records the range within each subgroup (the difference between the largest and smallest values). That range reflects how much the process outcome is varying from one observation to the next within those subgroups, so changes in the R chart indicate a change in dispersion or variability. Together, they separate shifts in the average from changes in variability, assuming each subgroup is the same size. The X-bar chart does not monitor the median, and the R chart does not monitor the mean or the variance individually, so the combination is specifically mean on the X-bar chart and range on the R chart.

In this type of control-chart approach, you’re looking at how a process behaves within small subgroups over time. The X-bar chart tracks the mean of each subgroup, so a drift or shift in the plotted points tells you the process center (the average level) may have changed. The R chart, on the other hand, records the range within each subgroup (the difference between the largest and smallest values). That range reflects how much the process outcome is varying from one observation to the next within those subgroups, so changes in the R chart indicate a change in dispersion or variability.

Together, they separate shifts in the average from changes in variability, assuming each subgroup is the same size. The X-bar chart does not monitor the median, and the R chart does not monitor the mean or the variance individually, so the combination is specifically mean on the X-bar chart and range on the R chart.