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Frequency Polygon


A graph which is used for understanding the shapes of distributions is known as a frequency polygon. A frequency polygon works as a histogram. It is useful for comparing the sets of data. A graph line is drawn by joining all the mid points of a top of a bar of a histogram. It is also useful for displaying the properties of cumulative distribution. Or, we can say that a frequency polygon is a closed figure, which is obtained by joining the middle points of the top of rectangles of histograms. The extreme values are joined with the x-axis at the half distance of class interval from the variable of the class interval.

In order to construct a frequency polygon, we have to follow some of the steps which are as follows:

Step 1: First, we have to take the middle point of a class interval on the x-axis.
Step 2: Then, we have to take the frequency on the y- axis.
Step 3: Now, we have to join the points which are obtained by x-axis and y-axis. Two extreme points are joined with the base in such a manner that they touch x-axis at half of the distance of the class interval outside the extreme points.

When we design the histogram and frequency polygon, we join the mid points which are situated on the top of the rectangles and the extreme points outside the rectangles. The relative frequency is related to the class intervals which can be shown with the help of frequency polygon. It also gives the ideas related to the shapes of the data distribution.

In a frequency polygon, the two end points always lie on the x- axis or it is a graphical display of a frequency table and the intervals of a frequency polygon are always shown on x-axis.
Frequency Polygon

Frequency Polygon Definition

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Frequency polygon is related to the geometry which is one of the branches of mathematics. To define frequency polygon, there is some related theory described below. Frequency polygon definition is based on histogram. Histogram is one of the frequency distributed graphs. Frequency polygon can be considered as a line graph, which is the result of sketching of the joining line of all the midpoints of a histogram located at the top.
If there is a data that is shaped using any frequency distributed graphs, then the frequency polygon provides the idea about the shape of that distributed data. The starting and ending two points of a frequency polygon always lie upon the horizontal axis that is x- axis. Suppose if we are drawing a graph that shows the number of vehicles that passes through a particular route in different hours, the flow of vehicles is a random phenomenon and the curve based on this data also would be random. But, if we are drawing for some particular hours, then the distributed data curve will show different values. But, the two points from where we are starting and the ending with the readings would lie on the x- axis. To draw the graph, we just need to draw a histogram of the data provided in the problem first and then a line graph is drawn through the midpoints of the top of the bars. Data totally depend upon the problem given in the question.

To solve the problem, the heights of the bars in the histogram are compared with the given values and then the midpoints of those bars are recognized and then a line graph is needed to be drawn. This is the needed frequency polygon.

Types of Graph

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Graph is defined as the representation of sets of data and objects where these objects can be connected or joined by links and represented in a particular format. Objects used are termed as vertices and for joining the vertices, links which are used are termed as edges. There are different types of graphs differentiated as line graphs, pictographs, cosmographs, flow charts, bar graphs, pie charts, organizational charts. These type of graphs are represented in different ways. Line graphs are very simple form of graph and it is represented in form of peaks and dips.

Lines in graph are raised and lowered according to the points of objects.
Frequency Polygon Definition

Second type of graph is pictographs which are defined as graphs or diagrams in which small pictures are used and information is compared. Third type of graph is termed as cosmographs and it is defined as a graph in which input and outputs are considered and data are compared. These types of graphs are also used for comparisons and makes easier to understand. Fourth type of graphical representation is termed as flow charts. It is defined as the representation of any information by dividing it further into small units. By dividing the information into smaller units, point to point data can be obtained. It helps a reader to understand in a easier way and basically used to represent the components of any information or data. Next type of graph is defined as bar graphs. These are very commonly used for representing data and information. Bar graphs are defined as graphs in which data is compared in the form of rectangular bars. These rectangular bars are represented in a form such that it lies vertical over X- axis.