The cumulative frequency gives us the number of observations lying below or above a particular value of a variable. Cumulative frequencies are of two types : a) Less than type, b) more than type.
- Less than type: We calculate the number of observations lying below each value of the variable. As the values increase we keep on adding the corresponding frequencies to get the cumulative frequency.
Example 1: The weights of 36 pumpkins from a vegetable market are recorded and presented as a frequency distribution table :
The table shows that there are 6 pumpkins weighing 4 kg, but there are 30 pumpkins weighing 4kg or less. Similarly there are 35 pumpkins having weight not more than 6kg.
This can be represented graphically as in figure 1.
Figure 1
- More than type: We calculate the number of observations lying above each value of the variable. We take the same example as above.
Example 2:
Example 3: Let us now consider the case where a teacher in a school assesses the performance of her students using the concept of cumulative frequency. In table 3 we show the marks obtained by 30 students in her class in Mathematics exam which was of 100 marks.
We can analyze the performance of the students from the table and the graph. We can see that 22 students have scored 60% or less. We can also study from the graph that 50% of the students (15) have secured 45% or less.
Bar Chart
Classified data is often represented diagrammatically as bar chart. Each class is represented by a rectangular bar. The bars are of equal width. The height of the bars indicates the magnitude of that particular class.
Example 4: Let us suppose a company named Technovations produces cell phones. We present different sales figures of the company using different charts and diagrams. In table 4 we represent the monthly sales figure of Technovations Company for the year 2013.The corresponding bar chart is shown in Figure 4.
Pie Diagram
The pie diagram or pie chart helps us to compare the different categories of a data series. The data is represented as a circle. Each sector of the circle corresponds to a category of the series. The angle of each sector is proportional to the magnitude of the corresponding category.
Histogram
Grouped frequency distributions of continuous variables are usually represented diagrammatically in the form of a Histogram. It consists of a set of adjoining rectangular bars. The areas of these rectangular bars are proportional to the corresponding frequency of the class that the bar represents.
In Table 6 we show the consumer income category wise sales in the year 2013 for our firm Technovations. Figure 6 represents this data in the form of a Histogram.
Frequency Polygon
Discrete data can be represented in the form of a frequency polygon. It is often seen as an alternative to a histogram. It can be used to represent continuous data as well. For grouped frequency distribution of equal class width, the frequencies are plotted against the mid point of each class. The points are then joined to get the polygon.
Example 7: The product sold by Technovations is divided into 5 categories according to their specifications. Table 7 shows the product category wise sales for 2013. Corresponding frequency polygon is shown in figure 7.
Bibliography:
Agresti, A. &Finlay, B.(1997). Statistical Methods for the Social Sciences. 3rd Eedition. Prentice Hall 1997.
Anderson, T.W. & Sclove, S.L.(1974). Introductory tatistical Analysis. Houghton Miffin Company, 1974.
Nagar, A.L. & Das, R.K.(2002). Basic Statistics. Oxford University Press. 2002.
Weiss, N.A. (1999). Introductory Statistics. Addison Wesley, 1999.
