A quality control supervisor wishes to determine whether the following measurements are random: $$\begin{array}{l}
\begin{array} { r r r r r r r r }
68.2 & 65 & 66.5 & 65 & 67.5 & 68 & 66 & 64.5 \
65.3 & 64.2 & 67.6 & 66.5 & 66.8 & 68.9 & 67 & 65 \
\hline\
\end{array}\
\begin{array} { r r r r r r r | }
\hline 65 & 67 & 68 & 71 & 68.5 & 63.6 & 64.7 \
71.5 & 70.7 & 66 & 68.5 & 70.5 & 69.5 & 70.1 \
\hline
\end{array}
\end{array}$$ For this purpose, the supervisor uses a previous median 67.9 and compares each measurement to the median.She determines that the number of runs is ______.
A)9
B)10
C)11
D)12
E)13

Question

A quality control supervisor wishes to determine whether the following measurements are random: $$\begin{array}{l}
\begin{array} { r r r r r r r r } 
68.2 & 65 & 66.5 & 65 & 67.5 & 68 & 66 & 64.5 \
65.3 & 64.2 & 67.6 & 66.5 & 66.8 & 68.9 & 67 & 65 \
\hline\
\end{array}\
\begin{array} { r r r r r r r | } 
\hline 65 & 67 & 68 & 71 & 68.5 & 63.6 & 64.7 \
71.5 & 70.7 & 66 & 68.5 & 70.5 & 69.5 & 70.1 \
\hline
\end{array}
\end{array}$$ For this purpose, the supervisor uses a previous median 67.9 and compares each measurement to the median.She determines that the number of runs is ______.
A)9
B)10
C)11
D)12
E)13

Quizplus · Accepted Answer

A run is a sequence of similar items (in this case, measurements above or below the median) followed or preceded by items of a different type. Using the median of 67.9, we classify each measurement as either above (+) or below (-) the median. The sequence of measurements relative to the median 67.9 is as follows: - - - - - - - - - - - + + + + + - + + + + + + - - - - - - - - - + + + + + + + + + + +. Counting the changes from "-" to "+" or "+" to "-" gives us 11 runs.

A Quality Control Supervisor Wishes to Determine Whether the Following