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Chapter 12: Problem 45

Describe how to construct a frequency polygon from a histogram.

Short Answer

Expert verified
A frequency polygon can be constructed from a histogram by first identifying the midpoint of each class interval from the histogram. The midpoints then represent the x-coordinates while the corresponding frequencies represent the y-coordinates in the polygon. Finally, it is best practice to extend the lines of the polygon to meet the x-axis at zero on both ends to visually close the polygon.

Step by step solution

01

Understanding the Histogram

Review the given histogram. The histogram consists of rectangular bars where each class interval is represented by a bar whose height corresponds to the frequency of that interval.
02

Mid-point calculation

Calculate the mid-point of each class interval. This could be done by adding the lower and upper boundaries of an interval and then dividing by two. The resulting points will represent corresponding classes in the frequency polygon.
03

Plotting the Frequency Polygon

Using the frequencies from the histogram and midpoints calculated in the previous step, plot a graph. The x-axis will represent the midpoints, and the y-axis will represent the frequencies. Connect each point that corresponds to a class midpoint and its frequency with a straight line.
04

Connecting to the Axes

To conclude the frequency polygon, extend the lines to reach zero on both ends of the frequency scale. This step visually closes the polygon and separates it from other surrounding lines and polygons.
05

Verification and Labeling

Review and label the x-axis and y-axis appropriately. The x-axis typically represents the class midpoints, and the y-axis represents the frequencies. Also, ensure that the frequency polygon correctly represents the data in the original histogram.

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