Explain how to draw a histogram with the provided data and identify the class width.

The adjusted class boundaries and frequencies are:

• 0-24: Adjusted class: $-0.5 - 24.5$, Class width: $24.5 - (-0.5) = 25$, Frequency: 9
• 25-49: Adjusted class: $24.5 - 49.5$, Class width: $49.5 - 24.5 = 25$, Frequency: 14
• 50-74: Adjusted class: $49.5 - 74.5$, Class width: $74.5 - 49.5 = 25$, Frequency: 7
• 75-99: Adjusted class: $74.5 - 99.5$, Class width: $99.5 - 74.5 = 25$, Frequency: 6
• 100-124: Adjusted class: $99.5 - 124.5$, Class width: $124.5 - 99.5 = 25$, Frequency: 8
• 125-149: Adjusted class: $124.5 - 149.5$, Class width: $149.5 - 124.5 = 25$, Frequency: 10
• 150-174: Adjusted class: $149.5 - 174.5$, Class width: $174.5 - 149.5 = 25$, Frequency: 6

Since all class widths are equal (25 km), the height of each bar in the histogram will be directly proportional to its frequency.

1. Draw a horizontal axis (x-axis) and label it "Distance (in km)". Mark the adjusted class boundaries: $-0.5, 24.5, 49.5, 74.5, 99.5, 124.5, 149.5, 174.5$.
2. Draw a vertical axis (y-axis) and label it "Number of villages" (Frequency). Scale this axis from 0 up to at least 14 (the maximum frequency).
3. For each class interval, draw a rectangular bar. The base of each bar should span its adjusted class interval on the x-axis, and its height should correspond to the frequency on the y-axis. The bars should touch each other, as this is a histogram for continuous data.

Here's a description of the bars you would draw:

• Bar 1: Base from $-0.5$ to 24.5, Height: 9
• Bar 2: Base from 24.5 to 49.5, Height: 14
• Bar 3: Base from 49.5 to 74.5, Height: 7
• Bar 4: Base from 74.5 to 99.5, Height: 6
• Bar 5: Base from 99.5 to 124.5, Height: 8
• Bar 6: Base from 124.5 to 149.5, Height: 10
• Bar 7: Base from 149.5 to 174.5, Height: 6

This will create the required histogram.