7) (8 pts)

Construct a histogram and a frequency polygon for the following frequency distribution

Miles

Miles Number of Commuters
Class Frequency
0 - 24 4
25 - 49 10
50 - 74 11
75 - 99 5
100 –124 1

No data, no histogram. In any case, we don't have the tools to draw polygons

Miles Number of Commuters

Class Frequency
0 - 24 4
25 - 49 10
50 - 74 11
75 - 99 5
100 –124 1

To construct a histogram and a frequency polygon for the given frequency distribution, follow these steps:

1. First, create a table to organize the data:

Miles Class Frequency
0 - 24 4
25 - 49 10
50 - 74 11
75 - 99 5
100 – 124 1

2. Determine the class width by subtracting the lower limit of one class from the lower limit of the next class. In this case, we have a class width of 25 (24 - 0 = 25).

3. Create a horizontal axis for the histogram with the appropriate scale and label it "Miles."

4. Plot rectangles for each class on the horizontal axis, with the height of each rectangle representing the frequency of that class.

- For the first class, 0-24, plot a rectangle with a height of 4.
- For the second class, 25-49, plot a rectangle with a height of 10.
- For the third class, 50-74, plot a rectangle with a height of 11.
- For the fourth class, 75-99, plot a rectangle with a height of 5.
- For the fifth class, 100-124, plot a rectangle with a height of 1.

5. Label each rectangle with its respective class limits (0-24, 25-49, etc.).

6. Title the graph as "Histogram of Commuters' Miles" or something similar.

To create a frequency polygon:

7. Start by plotting the midpoint of each class on the vertical axis and the corresponding frequency on the horizontal axis.

- The midpoint for the first class (0-24) is (24 + 0) / 2 = 12.
- The midpoint for the second class (25-49) is (49 + 25) / 2 = 37.
- The midpoint for the third class (50-74) is (74 + 50) / 2 = 62.
- The midpoint for the fourth class (75-99) is (99 + 75) / 2 = 87.
- The midpoint for the fifth class (100-124) is (124 + 100) / 2 = 112.

8. Connect the plotted points to form a line graph.

9. Extend the lines to the vertical axis (y-axis) and horizontal axis (x-axis) to create a polygon.

10. Label the x-axis as "Miles" and the y-axis as "Frequency."

11. Title the graph as "Frequency Polygon of Commuters' Miles" or something similar.

That's it! You've successfully constructed a histogram and a frequency polygon for the given frequency distribution.