9. A random survey of 100 cars found the following frequency distribution for the fuel efficiency of the car, as measured in miles per gallon. Construct a histogram below that effectively shows the distribution of this data set.
\begin{tabular}{|c|c|} \hline \begin{tabular}{c} Fuel Efficiency \\ (miles per gallon) \end{tabular} & Number of Cars \\ \hline 10 to 14 & 4 \\ \hline 15 to 19 & 17 \\ \hline 20 to 24 & 36 \\ \hline 25 to 29 & 24 \\ \hline 30 to 34 & 10 \\ \hline 35 to 39 & 6 \\ \hline 40 to 44 & 3 \\ \hline \end{tabular}
Sure, let's construct a histogram for the given frequency distribution of fuel efficiency (measured in miles per gallon) among 100 cars. We'll follow these steps:
1. Identify the Categories and Frequencies: First, we list out the categories and their corresponding frequencies: - 10 to 14 miles per gallon (mpg): 4 cars - 15 to 19 mpg: 17 cars - 20 to 24 mpg: 36 cars - 25 to 29 mpg: 24 cars - 30 to 34 mpg: 10 cars - 35 to 39 mpg: 6 cars - 40 to 44 mpg: 3 cars
2. Data Representation: We can represent this data in the form of a histogram where the x-axis represents the fuel efficiency categories and the y-axis represents the number of cars.
3. Final Histogram Data: The resulting histogram data will be: - 10-14: 4 - 15-19: 17 - 20-24: 36 - 25-29: 24 - 30-34: 10 - 35-39: 6 - 40-44: 3
4. Construct the Histogram: You can use these steps to draw the histogram either by hand or using a graphing tool/software.
### Histogram: - Draw a horizontal axis (x-axis) and label it with the fuel efficiency ranges. - Draw a vertical axis (y-axis) and label it with the number of cars. - Draw bars for each category. The height of each bar should correspond to the number of cars in that category.
Below is a rough sketch of how the histogram will look:
``` Number of Cars | | x | x | x | x | x x | x x x | x x x | x x x x | x x x x | x x x x x | x x x x x | x x x x x x | x x x x x x x | x x x x x x x |___x_____x___x___x___x__x_x__x_x__x__x___x____Fuel Efficiency (mpg) 10-14 15-19 20-24 25-29 30-34 35-39 40-44 ```
In the histogram: - The first bar represents the category 10-14 mpg and its height is 4. - The second bar represents the 15-19 mpg category and its height is 17. - The third bar represents the 20-24 mpg category and its height is 36. - The fourth bar represents the 25-29 mpg category and its height is 24. - The fifth bar represents the 30-34 mpg category and its height is 10. - The sixth bar represents the 35-39 mpg category and its height is 6. - The seventh bar represents the 40-44 mpg category and its height is 3.
This histogram effectively shows the frequency distribution of the fuel efficiency of the surveyed cars.
