This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — To draw a histogram, we first need to adjust the class boundaries to make them continuous. Since the data is given in discrete intervals (e.g., 0-24, 25-49), there's a gap of 1 unit between the upper limit of one class and the lower limit of the next. We adjust this by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class. Step 1: Adjust class boundaries and determine 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. Step 2: Draw the histogram. 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. What's next?