An $\bar { x }$ chart is being developed using 15 samples of size 9 each.The average of 15 sample means is 6.20.The average of the 15 ranges is 0.30.The upper control limit is _______________.
A)6.301
B)6.267
C)6.133
D)6.099
E)6.312

Question

Quizplus · Accepted Answer

The upper control limit (UCL) for an $\bar{x}$ chart is calculated using the formula: $$UCL = \bar{x} + A_2 \times \bar{R}$$ where $\bar{x}$ is the average of the sample means, $\bar{R}$ is the average range of the samples, and $A_2$ is a factor that depends on the sample size. For a sample size of 9, $A_2$ is typically 0.337. Plugging in the given values: $$UCL = 6.20 + 0.337 \times 0.30 = 6.20 + 0.1011 = 6.301$$

An xˉ\bar { x }xˉ Chart Is Being Developed Using 15 Samples of Size 9

An $\bar { x }$ Chart Is Being Developed Using 15 Samples of Size 9