# Type of Graphs

**Introduction - GRAPHS**

It is important to familiar with different types of graphs, because data can be represented in various ways. Sometimes bar charts and pie charts are used, but at others pyramids and other pictorial representation will be used, so the student must be familiar with all types of pictorial representation. We give below different types of graphs and the best way to solve them.

** **

**Type of Graphs**

Graphs can be divided into natural scale graphs and ratio scale graphs. The natural scale graphs can broadly be divided into two types - (i) Time Series Graphs, and (ii) Frequency Graphs.

** **

# Time Series Graphs

**Time Series Graphs**: The time series graphs have a time variable, e.g., years, months of the X-axis and one or more variables dependent on the Y-axis. A suitable scale has to be devised for presenting both the variables.

**(i) Line Graphs: **here separate lines represent the variables with reference to the time. The following graph shows the mortality rates per lakh population by tuberculosis for 1920 to 1970.

The above graph shows how TB deaths per lakh population have been going down over the years. The rate of decrease as also the years with the maximum decrease or the least decrease can be found out. These will be the typical questions for this type of graph.

**(ii) Band Graphs: **In this type of graph, various phenomena which form part of the whole are shown by successive bands or components to enable an overall picture along with the successive contributions of the components. The following graph shows the number of vehicles registered in a particular year. The width of the bands of each represents the number of cars, scooters or motorcycles that have been registered.

# Frequency Graphs

**Frequency Graphs**

In a frequency graph the size or the value of the item is represented on the horizontal axis and the frequency or the number of items on the vertical axis. The most commonly used frequency graphs are discussed below:

**Line Graph:** Under this, the height of the straight line on each size of item indicates the concentration of frequency in that class. This is appropriate in case of discrete frequency distribution where a given frequency is associated with a given value only and not a range of values.

**Histogram:** This graph is used for continuous frequency distribution. The widths of the class-intervals are marked along the X-axis. Rectangles of areas proportional to the frequencies of the respective class-intervals are erected. If the class-intervals are of equal lengths, then the heights of the rectangles are proportional to the corresponding frequencies and for rectangles are proportional to the ratios of the frequencies to the width of the corresponding class.

The typical questions on the above graph could be: (a) ratio of sales of 3^{rd} quarter to those of say first quarter (given by 90/20.4 so it calls for some approximation); (b) percentage growth of sales from second to third quarter (given by [3^{rd} quarter - 2^{nd} quarter sales]/2^{nd} quarter sales; (c) average sales per month for the company over the year (given by adding up the figures and dividing by 12).

Students are advised to do some “number crunching” and look at such charts in the financial papers and do such calculations on their own.

# Frequency Polygon and Frequency Curve

**Frequency Polygon and Frequency Curve:** The values of the variate for an ungrouped data are taken as the abscissa and their frequencies are taken as the ordinates. For a grouped data, the mid-points of the class-intervals are taken as the abscissa. Then a frequency polygon is obtained by joining the plotted points by the straight lines. If the class-intervals are of small length, the plotted points are joined by free hands. The curve so obtained is known as frequency curve. Frequency polygon for equal class-intervals can be obtained by joining all the mid-points of the upper sides of rectangles, of the histogram, by straight lines.