Frequency Distribution Graph Explained

The question asks to identify the type of graph created by plotting frequency density on the vertical axis against the mid-points of the classes on the horizontal axis.

Analyzing Graph Options

Let's look at the different types of graphs mentioned and see which one fits the description:

• Pie diagram: This type of diagram represents data as slices of a circle, showing proportions of a whole. It's not suitable for plotting frequency density against class mid-points.
• Bar diagram: Bar diagrams use rectangular bars to represent data, typically showing frequencies for different categories or discrete values. While related to frequency, they don't specifically plot frequency density against class mid-points in the way described.
• Frequency polygon: A frequency polygon is specifically constructed by plotting points corresponding to the frequency (or frequency density) of each class interval at its mid-point. These points are then connected by straight lines. This directly matches the definition given in the question.
• Sub-divided bar diagram: This is a variation of the bar diagram used to show how a total is divided into parts within each category. It doesn't fit the requirement of plotting frequency density against class mid-points.

Understanding the Frequency Polygon

A frequency polygon is a graphical technique used in statistics to visualize the shape of a distribution. Here's how it relates to the question:

• Axes: The horizontal axis (x-axis) represents the mid-points of the class intervals. The vertical axis (y-axis) represents the frequency density (or sometimes just the frequency, especially if class intervals are equal).
• Construction: Points are plotted where the frequency density for a class interval meets its corresponding mid-point.
• Connection: These plotted points are then joined by straight line segments. Often, the polygon is closed by joining the first and last points to the x-axis at the mid-points of the preceding and succeeding class intervals (which are assumed to have zero frequency).

Therefore, a graph constructed by plotting the frequency density against the mid-points of the class is a frequency polygon.