GRAPHICAL REPRESENTATION OF DATA

GRAPHICAL REPRESENTATION OF DATA

We have discussed the representation of data in tabular form. There is another representation known as graphical representation of data.

These representations become easier than tabular form. We have the following graphical representation :

(a) Bar graphs

(b) Histograms

(c) Frequency polygons.

BAR GRAPHS:

A bar graph is a pictorial representation of data in which usually bar of uniform width are drawn with equal spacing between them on one axis and values of variable are shown on other axis.

Each rectangle or bar represents only one value of the data. So, the number of rectangles will be exactly the same as the number of values in the numerical data. The height (or length in case the base is on a vertical line) of each bar is proportional to the numerical values of the data. The height/length of each bar represents the numerical values of the data on a scale, selected suitably.

HISTOGRAMS:

This is a form of representation like the bar graph, but it is used for continuous class intervals.

For a continuous frequency distribution, a series of rectangles are constructed having their widths equal to the widths of the classes and heights (or lengths) are selected in such a way that, the areas of the rectangles are respectively proportional to the frequencies of the classes. In case, the widths of the classes are uniformly same, the heights of the rectangles are selected proportional to the corresponding frequencies of the classes. By selecting suitable scales on x-axis and y-axis, the rectangles are drawn leaving no gap in between consecutive rectangles. The figure drawn appears like a single solid figure and it is called a histogram.

FREQUENCY POLYGONS:

It is another representation in which we join upper midpoint of all the rectangles. The polygon so formed is called Frequency polygon.

Frequency polygon of a given continuous frequency distribution can be drawn in two ways :

• With the help of the histogram of the given frequency distribution. 
• Without taking the help of the histogram.

question In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained :

Observe the bar graph given above and answer the following questions :

(i) How many students were born in the month of November ?

(ii) In which month were the maximum number of students born ?

Solution: (i) 4 students were born in the month of November.

(ii) The Maximum number of students were born in the month of August.

question A family with a monthly income of Rs 20,000 had planned the following expenditures per month under various heads :

Draw a bar graph for the data above.

Solution: The bar graph is drawn in figure.

question Consider the marks, out of 100, obtained by 51 students of a class in a test, given in Table.

Draw a frequency polygon corresponding to this frequency distribution table.

Solution:

question In a city, the weekly observations made in a study on the cost of living index are given in the following table :

Draw a frequency polygon for the data above (without constructing a histogram).

Solution:

question Five political parties namely A, B, C, D and E contested an election for 80 seats in a house. The parties won 20 seats, 30 seats, 5 seats, 15 seats and 10 seats respectively. Represent the data as a simple bar diagram.

Solution: