Paper 4: Fundamentals of Business Mathematics & Statistic

4.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Statistical Representation of Data

4.3 GRAPHICAL REPRESENTATION OF FREQUENCY DISTRIBUTION

4.3.1. HISTOGRAM (when C.I. are equal)

Frequency distribution can be presented in the graphical form. Such graphs are easily perceived by the

mind and gives a birds eye view and they are more appealing than the tabulated data. The graph also

helps in comparative study of two or more frequency distributions with regards to their shapes and patterns.

The most commonly used graphs for charting a frequency distribution are as follows –

Histogram

This graphical method is most widely used in practice. Histogram is a series of adjacent vertical bars whose

height is equal to the frequencies of the respective classes & width is equal to the class interval.

Construction of Histogram – While constructing Histogram the variable taken on X-axis & frequency of Y-

axis.

(i) Histogram with equal classes – When class intervals are equal, take the frequency on Y-axis and the

variable on X-axis and adjacent rectangles are constructed. The height of these rectangles would be

exactly equal (or proportional) to the frequency of the given class.

(ii) Histogram with unequal classes – If the classes are not uniform, then frequencies have to be adjusted

by the adjustment factor.

First find the class having the lowest class interval. This is taken as the starting point.

Adjustment factor = Lowest width of class in the seriesWidth/magnitude of the class

Adjusted frequency of a class =

Given frequency

Adjustment factor

For e.g. the class interval in 70 – 90 its width is 20. If the lowest width in the series is 5, then the adjustment

factor is 20/5 = 4 & the corresponding frequency would be divided by 4 to get the required adjusted

frequency needed for the graph.

If only midpoints are given then upper & lower limits of various classes have to be calculated & then only

histogram would be constructed.

Frequency Polygon

Frequency polygon could be drawn by first drawing histogram & then joining all the midpoints of the tops

(upper side) of the adjacent rectangle of the histogram by straight line graphs. The figure so obtained is

called a frequency polygon. It should be noted that it is necessary to close the polygon at both ends by

extending them to the base line so that it meets the X-axis at the mid points of the two hypothetical classes

i.e. the class before the first class & the class after the last class having the zero frequency.

Frequency polygon could alternatively be drawn without first drawing the histogram. This could be done

by plotting the frequencies of different classes (along Y-axis) against the mid values of corresponding classes

(along X axis). These points are joined by straight line to get a frequency polygon. Here also this polygon

would be closed at both ends by extending them to meet the X-axis.