This question: 1 point(s) possible
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 46.6 miles per hour.
Speed (miles per hour)
Frequency
\begin{tabular}{ccccc}
$42-45$ & $46-49$ & $50-53$ & $54-57$ & $58-61$ \\
\hline 26 & 14 & 6 & 3 & 2
\end{tabular}

The mean of the frequency distribution is $\square$ miles per hour.
(Round to the nearest tenth as needed.)
Which of the following best discribes the relationship between the computed mean and the actual mean?
A. The computed mean is not close to the actual mean because the difference between the means is more than $5 \%$.
B. The computed mean is not close to the actual mean because the difference between the means is less than $5 \%$.
C. The computed mean is close to the actual mean because the difference between the means is less than $5 \%$.
D. The computed mean is close to the actual mean because the difference between the means is more than $5 \%$.

Step 1 ：First, we need to find the midpoints of each speed range. The midpoints are \(43.5, 47.5, 51.5, 55.5, 59.5\).

Step 2 ：The frequencies for each speed range are given as \(26, 14, 6, 3, 2\).

Step 3 ：We calculate the mean of the frequency distribution by multiplying each midpoint by its frequency, summing these products, and then dividing by the total number of values. The total sum of these products is \(2390.5\).

Step 4 ：The mean of the frequency distribution is then calculated as \(\frac{2390.5}{51}\), which gives us a mean of \(46.872549019607845\).

Step 5 ：We round this to the nearest tenth to get a mean of \(46.9\) miles per hour.

Step 6 ：The actual mean is given as \(46.6\) miles per hour.

Step 7 ：We calculate the difference between the computed mean and the actual mean to be \(0.27254901960784395\).

Step 8 ：We then calculate the percentage difference between the computed mean and the actual mean to be \(0.5848691407893647\) percent.

Step 9 ：Since the percentage difference is less than \(5\%\), we can say that the computed mean is close to the actual mean.

Step 10 ：Final Answer: The mean of the frequency distribution is \(\boxed{46.9}\) miles per hour. The computed mean is close to the actual mean because the difference between the means is less than \(5\%\).