Use the grouped data formulas to find the indicated mean or standard deviation.
-The manager of a bank recorded the amount of time a random sample of customers spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results.
Approximate the sample mean. Round your answer to one decimal place.
714 $$\begin{array} { c | c }
\begin{array} { c }
\text { Waiting time } \
\text { (minutes) }
\end{array} & \begin{array} { c }
\text { Number of } \
\text { customers }
\end{array} \
\hline 0 - 3 & 12 \
4 - 7 & 14 \
8 - 11 & 13 \
12 - 15 & 6 \
16 - 19 & 8 \
20 - 23 & 2 \
24 - 27 & 1
\end{array}$$ 312
A)9.1 min
B)13.5 min
C)8.0 min
D)9.2 min

Question

Use the grouped data formulas to find the indicated mean or standard deviation.
-The manager of a bank recorded the amount of time a random sample of customers spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results.
Approximate the sample mean. Round your answer to one decimal place.
714 $$\begin{array} { c | c } 
\begin{array} { c } 
\text { Waiting time } \
\text { (minutes) }
\end{array} & \begin{array} { c } 
\text { Number of } \
\text { customers }
\end{array} \
\hline 0 - 3 & 12 \
4 - 7 & 14 \
8 - 11 & 13 \
12 - 15 & 6 \
16 - 19 & 8 \
20 - 23 & 2 \
24 - 27 & 1
\end{array}$$ 312
A)9.1 min
B)13.5 min
C)8.0 min
D)9.2 min

Quizplus · Accepted Answer

The sample mean for grouped data is calculated using the formula: $\bar{x} = \frac{\sum (f \cdot m)}{n}$, where $f$ is the frequency, $m$ is the midpoint of each class, and $n$ is the total number of observations. Calculating the midpoints and applying the formula gives a mean of approximately 9.1 minutes.

Use the Grouped Data Formulas to Find the Indicated Mean