Organisation and Graphical Presentation of Data

It refers to the systematic arrangement of collected data, so that the data becomes easy to understand and more convenient for further statistical treatment.

Classification is the process of arranging data into sequences and groups according to their common characteristics and separating into different but related parts.

Data is a team used for discribing an attribute about the activities of a business or person or any other living or non-living thing. Data can be any fact, observation, assumption or occurance.
E.g.- Name, date, height, weight, age, scores, percentage, grades etc.

Methods of Organising and Presenting Data -

In general the following four methods are used for organising and presenting statistical data -

Presentation in the form of Statistical Tables
Presentation in the form of frequency Distribution
Graphical presentation of ungrouped data
Graphical presentation of frequency Distribution (Grouped data)

1. Presentation in the form of Statistical Tables

The data are tabulated or arranged in some properly selected classes and the arrangement is described by title and subtitles. Such tables can list the original raw data as well as the percentages, means, standard deviations etc.

2. Presentation in the form of Frequency Distribution

We group the quantitative data into some arbitrarily chosen classes.

Usually the scores are distributed into groups of scores (classes) and each score is allotted a place in the respective class. It is also seen how many times a particular score or class occurs in the given data. This is known as frequency of a score or class.

Thus frequency distribution may be considered as a method of presenting a collection of groups of scores in such a way as to show the frequency in each group of scores or class.

Various steps for presenting quantitative data by a frequency distribution are as following -

Steps for grouping data into frequency Distribution -

1. Range -

Range can be found out by subtracting the lowest score from the highest.

Range in example = 68 - 21 = 47

2. Class interval -

Total size of a class or group, denoted by 'i'

After finding range, the number and size of the classes used in grouping data are decided.

It can be done in two ways -

First decide the no. of class then find the class interval. Usually, not fewer than 10 or more than 20 classes are used.
i = Range / no. of classes desired
Class interval is always a whole number.
First decide the class interval then find the no. of classes. Usually, class intervals of 2, 3, 5 or 10 units are used.
No. of classes = Range/Class interval

In given example,

no. of classes taken = 10
then, class interval = 5

3. Writing the content of frequency distribution -

Here, first we write the classes of distribution, then we tally the scores into proper classes and finally we check the total of frequencies with the total data taken.

Here total frequency of 50 is equal to the total no. of students.

Some more things regarding a frequency distribution -

1. Class limits -

The designation of classes, i.e., 21-25, 26-30 etc. are called the indicated or written class limits. The actual class limits are always taken as 0.5 units below and 0.5 units above the written class limits.

Actual limits of class 21-25 is 20.5-25.5

2. Mid-point of a class

Mid-point of a class = Lower limit + (Upper limit - lower limit) / 2

We don't consider actual class limits in calculating mid-point.

Mid-point of class 21-25 is 21 + (25 - 21) / 2 = 21 + 4/2 = 21 + 2 = 23

3. Graphical presentation of Frequency Distribution (Grouped data)

There are four methods of representing a frequency distribution graphically -

The Histogram or column diagram
The Frequency Polygon
The Cumulative frequency Graph
The Cumulative frequency Percentage Curve or Ogive

1. The Histogram or Column Diagram

A histogram is essentially a bar graph of a frequency distribution. The following point are to be kept in mind -

The scores in the form of actual class limits are taken
i.e. - 20.5-25.5
Two extra classes are taken - one above and one below
i.e.- 15.5-20.5 and 70.5-75.5
Now plot the actual lower limits of classes on x-axis and the frequencies on y-axis.
Each class with its specific frequency is represented by a separate rectangle.
A good general rule for selecting units on x and y axis is that make the height of figures approx. 75% of its width.

2. The Frequency Polygon

A frequency polygon is essentially a line graph of a frequency distribution. The following point are to be kept in mind -

To draw a frequency polygon from a histogram, connect the mid-points of the upper bases of the rectangles.

We can also directly draw frequency polygon as following -

Two extra classes are taken - one above and one below
i.e. 16-20 and 71-75
Find the mid-points of all classes and plot them on x-axis while plotting frequencies on y-axis.
The various points detained from each class and its specific frequency are joined by straight line.
A good general rule for selecting units on x and y axis is that make the height of figures approx. 75% of its width.

A frequency polygon is a closed curve while a frequency curve is not a closed curve. In frequency curve we do not take two extra classes.

3. The Cumulative Frequency Curve or Graph

The cumulative frequency curve is essentially a line graph of actual upper limits of a class and their respective cumulative frequencies. The following points are to be kept in mind -

Calculate the cumulative frequency by successively adding the individual frequency starting from lowest class.
One extra class is taken at the lower end.
i.e.- 16-20.
Plot the graph with actual upper limits of class at x-axis and cumulative frequency at y-axis.

4. The Cumulative Percentage Frequency Curve or Ogive

The cumulative percentage frequency curve is essentially a line graph of actual upper limits of a class and their respective cumulative percentage frequencies. The following points are to be kept in mind -

Calculate the cumulative percentage frequency by multiplying the cumulative frequency by 100/N, where N is total frequency.
Here, 100/N = 100/50 = 2
One extra class is taken at the lower end.
i.e.- 16-20
Plot the graph with actual upper limits of class at x-axis and cumulative percentage frequency at y-axis.