Frequency Polygon

Definition

A frequency polygon is a graphical representation of the frequency distribution of a set of data. It is a broken-line graph that connects the midpoints of the tops of adjacent bars in a histogram, creating a polygon-like shape that illustrates the distribution of the data.

5 Must Know Facts For Your Next Test

1. Frequency polygons are useful for comparing the distributions of two or more datasets, as they allow for the visual identification of differences in shape, central tendency, and variability.
2. The vertices of a frequency polygon are located at the midpoints of the tops of the histogram bars, and the line segments connect these vertices to form the polygon-like shape.
3. Frequency polygons are particularly helpful for visualizing the distribution of continuous data, as they can smoothly represent the shape of the distribution, unlike a histogram which may have gaps between the bars.
4. The area under a frequency polygon is equal to the total frequency of the data, just as the area under a histogram is equal to the total frequency.
5. Frequency polygons can be used to identify the modality (number of peaks) of a distribution, as well as the symmetry or skewness of the data.

Review Questions

• Explain how a frequency polygon relates to a histogram and how it can be used to compare the distributions of two or more datasets.
  • A frequency polygon is closely related to a histogram, as it is derived from the same underlying frequency distribution data. While a histogram displays the frequency of data points within discrete bins, a frequency polygon connects the midpoints of the tops of the histogram bars to create a continuous, polygon-like shape. This allows for the visual comparison of the distributions of two or more datasets, as the shape, central tendency, and variability of the data can be more easily identified and compared between the frequency polygons.
• Describe the key features of a frequency polygon and how they can be used to analyze the characteristics of a data distribution.
  • The key features of a frequency polygon include the vertices, which are located at the midpoints of the tops of the histogram bars, and the line segments that connect these vertices to form the polygon-like shape. The shape of the frequency polygon can provide insights into the distribution of the data, such as the number of peaks (modality), the symmetry or skewness of the distribution, and the central tendency and variability of the data. Additionally, the area under the frequency polygon is equal to the total frequency of the data, just as the area under a histogram is equal to the total frequency.
• Explain how a frequency polygon can be used to visualize the distribution of continuous data and how it differs from a histogram in this regard.
  • Frequency polygons are particularly useful for visualizing the distribution of continuous data, as they can smoothly represent the shape of the distribution, unlike a histogram which may have gaps between the bars. This is because the line segments of the frequency polygon connect the midpoints of the histogram bars, creating a continuous, polygon-like shape that can more accurately represent the underlying distribution of the data. This makes frequency polygons advantageous for identifying the modality, symmetry, and other characteristics of continuous data distributions, which may be obscured or less apparent in a histogram representation.

Related terms

Histogram:

A histogram is a graphical representation of the frequency distribution of a dataset, where the data is grouped into bins or classes, and the height of each bar corresponds to the frequency or count of data points within that bin.

Time Series Graph:

A time series graph is a type of graph that displays data points over a period of time, allowing for the visualization of trends, patterns, and changes in a variable or multiple variables over time.

Frequency Distribution:

A frequency distribution is a tabular or graphical representation of the number of times each distinct value in a dataset occurs, providing information about the distribution of the data.