Ten samples of n = 5 were collected to construct an $\overline { x ^ { * } }$ chart. The sample mean and range for each sample are shown in the table below. $$\begin{array} { | c c c | c c c | }
\hline \text { Sample } & \text { Mean } & \text { Range } & \text { Sample } & \text { Mean } & \text { Range } \
\hline 1 & 215 & 15 & 6 & 224 & 21 \
2 & 204 & 20 & 7 & 205 & 27 \
3 & 160 & 10 & 8 & 184 & 12 \
4 & 226 & 19 & 9 & 207 & 16 \
5 & 232 & 24 & 10 & 212 & 17 \
\hline
\end{array}$$ Calculate the empirical centerline for the R chart.
A)20.8
B)17.2
C)18.1
D)19.4

Question

Ten samples of n = 5 were collected to construct an $\overline { x ^ { * } }$ chart. The sample mean and range for each sample are shown in the table below. $$\begin{array} { | c c c | c c c | } 
\hline \text { Sample } & \text { Mean } & \text { Range } & \text { Sample } & \text { Mean } & \text { Range } \
\hline 1 & 215 & 15 & 6 & 224 & 21 \
2 & 204 & 20 & 7 & 205 & 27 \
3 & 160 & 10 & 8 & 184 & 12 \
4 & 226 & 19 & 9 & 207 & 16 \
5 & 232 & 24 & 10 & 212 & 17 \
\hline
\end{array}$$ Calculate the empirical centerline for the R chart.
A)20.8
B)17.2
C)18.1
D)19.4

Quizplus · Accepted Answer

The empirical centerline for the R chart is the average of the sample ranges. The average of the sample ranges is (15+20+10+19+24+21+27+12+16+17)/10 = 18.1.

Ten Samples of N = 5 Were Collected to Construct x∗‾\overline { x ^ { * } }x∗

Ten Samples of N = 5 Were Collected to Construct $\overline { x ^ { * } }$