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.
