Statistical graphs – Frequency Polygon

Introduction

Having organized the data into a frequency distribution, you need to present them in graphical form. The purpose of graph in statistics is to convey the data to the viewers into pictorial form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1.      Statistical graphs can be used to analyse a data or described it.

2.       They are used to get the audience’s attention in a speaking presentation.

3.      They are also used to discover a pattern in a situation over a period of time.

4.      Statistical graphs are used to summarize a data.

The frequency polygon:

The frequency polygon is a graph that displays the data by using lines that connect point plotted for the frequencies at the midpoint of the classes. The frequencies are represented by the heights of the points. They are drawn to have zero frequencies. We note that, frequency polygon can also be drawn without the bars. See fig below:

The example below shows the procedure for constructing a frequency polygon.

Example one:

The following is a frequency distribution of masses of parcels in a local post office.

Mass kg	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99
No. Of parcels	2	4	7	8	11	9	5	4	3

a.       Draw a frequency polygon for the distribution.

Solution

Steps:

1.      Find the midpoints of each class. Recall that midpoints are found by adding the upper and lower boundaries and dividing by 2; (9.5 + 19.5) ÷ 2 = 14.5, (19.5 + 29.5) ÷ 2 = 24.5 and so on.

2.      Draw the x and y axes. Label the x axis with the midpoint of each class, and then use a suitable scale on the y axis for the frequencies.

3.      Using the midpoints for the x-values and the frequencies as the y-values, plot the points.

4.      Connect adjacent points with line segments. Draw line back to the x axis at the beginning and end of the graph, at the same distance that the previous and next midpoints would be located. See the table below.

Mass (kg)	Mid-mass (x)	Frequency
10-19	14.5	2
20-29	24.5	4
30-39	34.5	7
40-49	44.5	8
50-59	54.5	11
60-69	64.5	9
70-79	74.5	5
80-89	84.5	4
90-99	94.5	3

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