Calculations from 30 subgroups of 5 measurements each yielded an Sbar of 15. The lower and upper control limits for a standard deviation chart derived from these data are most nearly:

To determine the lower and upper control limits for a standard deviation chart based on subgroup data, it's important to understand how these limits are calculated. The standard deviation (Sbar) from the data is a key component.

In this case, the subgroup standard deviation is given as Sbar = 15. For a control chart for standard deviation, the upper and lower control limits are typically calculated using the following formulas:

1. The lower control limit (LCL) is often set to zero because standard deviation cannot be negative.

2. The upper control limit (UCL) is usually computed as Sbar multiplied by a specific constant derived from statistical tables that relate to the size of the subgroups. For a sample size of 5, this constant will depend on statistical values associated with the distribution of the sample means.

In this instance, we would typically see the upper control limit calculated as a function of Sbar and the appropriate constant derived from the sample size. Let’s assume the appropriate constant yields an UCL of approximately 31.34 when combined with the Sbar of 15.

Thus, with the LCL being zero and the UCL calculated to be about 31.34, the control limits for the standard deviation chart would indeed