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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}

Sagot :

GinnyAnsweridn
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.
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