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Presentation of Data

The data collected can be presented in the following two ways:

1. Raw data or ungrouped data.

2. Grouped data


Raw data or ungrouped data
The data obtained in original form is called raw data. The raw data can be arranged in anyone of the following ways.
 

(i) Serial order

(ii) Descending order

(iii) Ascending order

The raw data arranged in ascending order or in descending order of magnitude is known as an array.

 

Range : The difference of the highest and lowest values in the data is called the range of the data .

Let the heights of 25 employees in a office of L.I.C. be (in cms).
160, 162, 170, 171, 165, 166, 161, 159, 158, 175, 163, 162, 164, 166, 170, 172, 171, 170, 173, 180, 160, 165, 164, 163, 167.   


These data are called raw data.

In descending order, the data look as follows:
180, 175, 173, 172, 171, 171, 170, 170, 170, 167, 166, 166, 165, 165, 164, 164, 163, 163, 162, 162, 161, 160, 160, 159, 158.

In ascending order these data will be as follows:
158, 159, 160, 160, 161, 162, 162, 163,163, 164, 164, 165, 165, 166, 166, 167, 170, 170, 170, 171, 171, 172, 173, 175, 180.  

Observations can be arranged in ascending order or in descending order if they are less but it is difficult to arrange them in ascending or descending order if they are more.   
To make it easy, understandable and clear, we can tabulate data in the form of a table.  

To present data in the tabular form we have the following column.

1. Height
From lowest to highest.

2. Tally mark
One bar (vertical line) is drawn for each value of height in the column opposite to it. To facilitate, we record tally marks in the group of five, the fifth tally mark is drawn diagonally across the first four.
For example ||||= 9

 

3. Frequency
The no. of times an observation occurs is called frequency of the observation.

 

Height (cm)

Tally mark

Frequency

158

1

1

159

1

1

160

11

2

161

1

1

162

11

2

163

11

2

164

11

2

165

11

2

166

11

2

167

1

1

170

111

3

171

11

2

172

1

1

173

1

1

175

1

1

180

1

1


This method of presentation of data is known as frequency distribution. The height is known as variates and the number of employees who have same height is known as frequency.
 





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