subject: Graphical Presentation Of Data In Statistics [print this page] Introduction to graphical representation of data:
Statics is the collection, organization, and interpretation of data. The collected data can be easily analyzed by using graphs. It is well said that one picture is better than a thousand words. The transformation of data through visual methods like graphs is representation of data Usually comparisons among the individual items are best shown by means of graphs. The representation then becomes easier to understand than the actual data.
Different types of data representation that are frequently used:
1.Bar graphs
2.Histograms
3.Frequency polygons
4.Pie charts.
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Graphical Representation Using Bar Graphs:
A bar graph is a type of visual representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis (say, the x-axis), depicting the variable. The variable are plotted on the other axis (say, the y-axis) and the heights of the bars depend on the values of the variable.
A family with a monthly income of Rs 20,000 had planned the following expenditures per month under various heads
We draw the bar graph of this data in the following steps. Note that the unit in the second column is thousand rupees. So, 4 against grocery means Rs 4000.
1. We represent the Heads (variable) on the horizontal axis, we take equal widths for all bars and maintain equal gaps in between. Let one Head be represented by one unit.
2. We represent the expenditure (value) on the vertical axis. Since the maximum expenditure is Rs 5000, we can choose the scale as 1 unit = Rs 1000.
3. To represent grocery, we draw a rectangular bar with width 1 unit and height 4 units.
4. Similarly, other Heads are represented by a gap of unit width
Graphical Representation Using Histograms:
Histogram is a visual form of representation of a continuous frequency distribution i.e. grouped frequency distribution with no space between the rectangles when plotted. Traditionally, class-intervals are taken along the horizontal axis while the respective class frequencies are taken along the vertical axis. This is similar to bar graph, but it is used for continuous class intervals
Note:The areas of the rectangles are proportional to the frequencies.
Consider the frequency distribution of the weights of 36 students of a class shown in the table below:
Let us represent the data given above graphically as follows:
(i) We chose an appropriate scale on horizontal axis to represent the weights. We can choose the scale as 1 cm = 5 kg. Also, since the first class interval is starting from 30.5 and not zero, we show it on the graph by marking a kink or a break on the axis.
(ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Since the maximum frequency is 15, we need to choose the scale to accomodate this maximum frequency.
(iii) We now draw rectangles (or rectangular bars) of width equal to the class-size and lengths according to the frequencies of the corresponding class intervals. For example, the rectangle for the class interval 30.5 - 35.5 will be of width 1 cm and length 4.5 cm.
(iv) In this way, we obtain the graph.
Graphical Representation Using Frequency Polygon :
Frequency polygon is formed by joining midpoints of the tops the adjoining rectangles in the histogram
For the example above frequency polygon is
Graphical Representation Using Pie Chart:
Pie diagram is a way of graphical representation of data which can be easily analyzed.It is used to compare the value given to the total value.A pie chart is a circular chart divided into sectors, showing the proportions so that the length of the arc of each sector is proportional to the value it represents. it is also called as Divided Circle Diagram.
To calculate angles when the data given in values of the individual quantities. Then sum up the all the values of quantities to get total value and use the below formula.
angle = ('("Value given")/("Total value")' ) x 360
Example pie chart:
angle =
Use the below formula to calculate angles when the quantities are given in percentages
Procedure to calculate angles
Arrange the data and calculate angles for the given values using above formula.
If the values given in percentage then multiply it with 3.6(i.e, '360/100' ) to get angle of the corresponding sector.
Number of divisions to be made is equal to number of quantites.
Arrange the angles of the quantities in an increasing order
Draw a circle and join the centre of the circle to the circumference at some point.
6. And starting from that line mark the angles for each quantity in an order, and put the titles for the sector.
Suggestions
Make a circle of appropriate size not too big or too small
it is always good to start with smaller angle which helps in avoiding accumulation of error while plotting
