Graphical Representation

Graphical Representation:

Graphical representation is necessary in the field of education. To understand data and draw conclusion is possible. To make data simple and comprehensive.

Three types of graphical representation:

1.      Histogram

2.      Frequency Polygon

3.      Cumulative Frequency Curve

4.      Ogive

Points in preparing graph:

In graph X – axis is abscissa and y axis is ordinate. Class interval is on x –axis. Frequencies on y –axis. Meeting point of X & Y axis is always taken as zero. Scale should be sufficiently large. It is advisable to take convenient units to show on X & Y axis.

A)    Histogram:

In statistics a histogram is a graph that represents the class frequencies in frequency distribution by vertical rectangles.

                                                                                    - Simpson & Kalfk

Points to be kept in mind for histogram:

1.      X – axis represents class intervals.

2.      Y – axis represents frequencies

3.      Height of every rectangle is according to the frequencies of the class interval which it represent.

When to use it?

When you want to see the pattern of variation of a particular process, such as when you are describing a problem, or during data collection and analysis.

The steps to create a histogram include:

1. Gather the data about the variable you are interested in.
2. Look at the data and determine the categories or intervals you will use to organize the data. For example, if you are measuring the number of weeks it takes to receive an order of contraceptives, "number of weeks of waiting time" is the data category.
3. Construct a frequency table for your data. The frequency corresponds to the number of times each value is observed. Using the example of waiting time to receive an order of contraceptives, the frequency table might look like this:
4. To create the histogram, draw a horizontal and a vertical axis. The horizontal axis (X) shows the data categories (such as time, or a measurement, like weight). The vertical axis (Y) represents the frequency of the observations (the number of observations for each category).
5. For each category of data, draw a rectangle (without space between the rectangles). The width of the rectangle represents the interval between two groups, and the height represents the observed frequency.

When class interval is inclusive convert it into exclusive series

B)    Frequency Polygon:

Polygon means many angles. Figure which depicts frequency is called frequency polygon. Plain figure bounded by a number of straight line a figure of many angles. Midpoint is on X –axis and Frequency on Y – axis. Two extra class intervals are assumed. One on top with zero frequency and another on bottom with zero frequency. Frequencies of this class interval is shown with dotted line.

Steps for preparing Frequency Polygon:

1.      Assume two extra class intervals with zero frequency.

2.      Find midpoint of each class interval.

3.      Plot midpoint on X- axis.

4.      Plot frequencies on Y- axis.

5.      Join this points with straight line.

6.      Then join this with the base on midpoints of assumed class intervals.