Histogram
A histogram is a bar graph that represents the frequency distribution of a dataset. The data is divided into continuous intervals, known as bins or classes. Each bar in a histogram represents the frequency of data points within a specific interval. The height of each bar corresponds to the frequency or count of data points within that interval, and the width of the bar covers the entire interval.
Frequency Polygon
A frequency polygon is a line graph that represents a frequency distribution. It is constructed by plotting points at the midpoints of each class interval or bin, where the height of each point corresponds to the frequency of the interval. These points are then connected by straight lines to form a polygon. Unlike the histogram, which uses areas to represent frequencies, the frequency polygon uses lines and points.
Differences Between Histogram and Frequency Polygon
Graphical Representation
- Histogram: A histogram uses bars to represent intervals. Each bar covers the entire interval on the x-axis and its height represents the frequency of the interval.
- Frequency Polygon: A frequency polygon uses points plotted at the midpoints of each interval, which are then connected by lines to form a polygonal shape.
Visual Interpretation
- Histogram: The visual impression is one of continuous data within intervals, making it easy to see the density of data points.
- Frequency Polygon: The polygonal form can make it easier to compare different distributions, especially on the same graph.
Data Type Suitability
- Histogram: Best suited for numerical, interval, or ratio data.
- Frequency Polygon: Can be used for the same type of data but also useful for visual comparisons of multiple datasets.
Special Considerations
Choosing Between Histogram and Frequency Polygon
When choosing between a histogram and a frequency polygon, consider the following:
- Use a histogram when you need to emphasize the density and distribution of data within specific intervals.
- Use a frequency polygon when comparing multiple sets of data on the same graph or when focusing on the trend across intervals.
Constructing a Histogram
- Determine Intervals: Divide the range of data into equal-sized intervals.
- Count Frequencies: Count the number of data points within each interval.
- Plot Bars: Draw bars for each interval where the height of the bar represents the frequency.
Constructing a Frequency Polygon
- Determine Midpoints: Find the midpoint of each interval.
- Plot Points: Plot points at the height corresponding to the frequency for each midpoint.
- Connect Points: Connect the points with straight lines to form the polygon.
Applications and Examples
Histograms
- Example: A histogram can be used to display the test scores of students to understand the distribution of grades.
- Application: Commonly used in quality control to show distribution and variation in manufacturing processes.
Frequency Polygons
- Example: A frequency polygon can be used to compare the distribution of two different sets of data, such as test scores from different classes.
- Application: Used in exploratory data analysis to compare trends and patterns across datasets.
Historical Context
Origin
- Histogram: The histogram was first introduced by Karl Pearson, a key figure in the development of modern statistics, in the late 19th century.
- Frequency Polygon: The frequency polygon was developed as a complementary tool to the histogram to offer a clearer view of the distribution trend over intervals.
Related Terms
- Bar Chart: A graph that uses bars to represent categorical data.
- Frequency Distribution: A summary of how frequent each value or range of values occurs in a dataset.
FAQs
Why use a frequency polygon over a histogram?
Can histograms and frequency polygons be used interchangeably?
Summary
Histograms and frequency polygons are both valuable tools for visualizing frequency distributions, each with its unique advantages. Histograms use bars to represent data density within intervals, making it clear and easy to interpret frequency distributions. Frequency polygons, on the other hand, provide a clear view of trends and comparisons across multiple datasets. Understanding their differences, construction, and applications can significantly enhance data analysis and interpretation.
References
- Pearson, Karl. (1895). Contributions to the Mathematical Theory of Evolution.
- Anderson, T.W., & Sclove, S.L. (1978). An Introduction to the Statistical Analysis of Data. Addison-Wesley.
