Frequency Polygons MCQs Quiz | Class 9
This quiz covers Unit VI: Statistics for Class IX Mathematics (Code 041). It focuses on the construction and interpretation of frequency polygons, including drawing them from histograms or tables and understanding their properties. Submit your answers to check your score and download the PDF solution.
Overview of Frequency Polygons
A frequency polygon is a visual representation of the distribution of data. It is a line graph derived from a histogram or constructed directly from a frequency distribution table. It is particularly useful for comparing two different sets of data on the same graph.
Key Concepts
- Class Mark: The midpoint of a class interval. It is calculated as (Upper Limit + Lower Limit) divided by 2. This value serves as the representative x-coordinate for the polygon points.
- Coordinates: To plot a frequency polygon, we use points where the abscissa (x-axis) is the class mark and the ordinate (y-axis) is the corresponding frequency.
- Closing the Polygon: To complete the shape, we assume a class before the first interval and a class after the last interval, both with zero frequency. This brings the line down to the x-axis at both ends.
- Area: The area enclosed by the frequency polygon and the x-axis is equal to the area of the corresponding histogram.
Construction Methods
Method 1: Using a Histogram
Draw the histogram for the given data. Mark the mid-points of the upper horizontal sides of the rectangles. Join these mid-points by straight lines. Finally, join the start and end points to the x-axis at the mid-points of imaginary adjacent classes with zero frequency.
Method 2: Without Histogram
Calculate the class marks for each class interval. Plot points taking class marks on the x-axis and frequencies on the y-axis. Join these points with straight line segments. Close the polygon by adding fictitious classes at both ends with zero frequency.
Quick Revision
- Frequency polygons are used for continuous frequency distributions.
- They provide a better visual estimate of the trend of the data compared to histograms.
- When two frequency polygons are drawn on the same axes, it helps in comparing two datasets easily.
Practice Questions
- Find the class mark of the interval 150-160.
- If a frequency polygon starts at class mark 5 and ends at class mark 45, what is the class width if there are 4 actual classes?
- Why do we join the start and end points to the x-axis?
- Can a frequency polygon be drawn for ungrouped data directly?
- What is the relationship between the mode of the data and the peak of the frequency polygon?
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