$\text { Data Table A }$
$\begin{array}{|l|l|l|l|l|}
\hline \begin{array}{c}
\text { Sample } \
\text { Number }
\end{array} & \text { Item 1 } & \text { Item 2 } & \text { /tem 3 } & \text { /tem 4 } \
\hline 1 & 13.10 & 13.90 & 12.80 & 13.20 \
\hline 2 & 13.80 & 13.00 & 12.50 & 12.70 \
\hline 3 & 14.00 & 12.90 & 13.10 & 13.50 \
\hline 4 & 12.30 & 13.30 & 12.80 & 13.60 \
\hline 5 & 13.10 & 12.60 & 13.30 & 12.90 \
\hline 6 & 12.50 & 13.40 & 12.80 & 13.30 \
\hline 7 & 13.60 & 12.70 & 13.30 & 13.80 \
\hline 8 & 12.50 & 13.50 & 13.10 & 12.90 \
\hline 9 & 13.00 & 13.60 & 12.70 & 13.20 \
\hline 10 & 12.80 & 12.90 & 12.70 & 13.30 \
\hline
\end{array}$
-Refer to Data Table A.The lower control limit for the range chart is ______.
A)1.777
B)0.223
C)0
D)2.282

Question

Quizplus · Accepted Answer

To find the lower control limit for the range chart, we use the formula: LCL = D3(R-bar), where D3 is a constant based on the number of samples (in this case, D3=0), and R-bar is the average range calculated as R-bar = (R1 + R2 + ... + Rn)/n, where R1, R2, ..., Rn are the ranges for each sample. The ranges for each sample are calculated as the difference between the largest and smallest values in each sample.

Using the given data, we can calculate the ranges and their average as follows:

Sample 1: Range = 1.80
Sample 2: Range = 1.30
Sample 3: Range = 1.10
Sample 4: Range = 1.30
Sample 5: Range = 0.70
Sample 6: Range = 0.90
Sample 7: Range = 1.10
Sample 8: Range = 1.00
Sample 9: Range = 0.90
Sample 10: Range = 0.60

R-bar = (1.80 + 1.30 + 1.10 + 1.30 + 0.70 + 0.90 + 1.10 + 1.00 + 0.90 + 0.60)/10 = 1.00

Therefore, the lower control limit for the range chart is LCL = D3(R-bar) = 0. Note that since D3 is 0 for 10 samples, the range chart does not have a lower control limit.

Data Table A \text { Data Table A } Data Table A -Refer to Data Table A

$\text { Data Table A }$ -Refer to Data Table A