Page 143 - Maths Skill - 6

Data Handling and Presentation 141

The raw data can be arranged in anyone of the following ways.

(i) Serial order or Alphabetical order (iii) Descending order
(ii) Ascending order

The raw data when put in ascending or descending order of magnitude is called an array.
Let the marks obtained by 30 students of Class VI in class test, out of 50 marks according to their roll numbers be.

39, 25, 5, 33, 19, 21, 12, 41, 12, 21, 19, 1, 10, 8, 12, 17, 19, 17, 17, 41, 40, 12, 41, 33, 19, 21, 33, 5, 1, 21

If we arrange them in ascending or descending order, it gives us a slightly better picture. In ascending order, the
data look as follows.

1, 1, 5, 5, 8, 10, 12, 12, 12, 12, 17, 17, 17, 19, 19, 19, 19, 21, 21, 21, 21, 25, 33, 33, 33, 39, 40, 41, 41, 41

In descending order, the data will be as follows.
41, 41, 41, 40, 39, 33, 33, 33, 25, 21, 21, 21, 21, 19, 19, 19, 19, 17, 17, 17, 12, 12, 12, 12, 10, 8, 5, 5, 1, 1

If the number of observations is large, then to make it easily understandable and clear, we can tabulate data in the
form of a table.
In the first column of the table, we write all marks from lowest to highest. We now look at the first value in
the given raw data and put a bar (vertical line) in the second
column opposite to it. Now, we see the second value in the Marks Tally Marks No. of Students
given raw data and put a bar opposite to it in the second column. 1 || 2
This process is repeated till all observations in the given raw 5 || 2
data are exhausted. The bars drawn in the second column are 8 | 1
known as tally marks and to facilitate we record tally marks 10 | 1
in bunches of five, fifth tally mark is drawn diagonally across 12 |||| 4
the first four as . 17 ||| 3
For example, = 7. We finally count the number of tally 19 |||| 4
marks corresponding to each observation and write in the third 21 |||| 4
column. 25 | 1
This way of presentation of data is known a frequency 33 ||| 3
distribution. Marks are called variates and the number of 39 | 1
students who have secured a particular number of marks is 40 | 1
called frequency of the variate. The number of times an 41 ||| 3
observation occurs in the given data is called the frequency of Total 30
the observation.

Fact-o-meter

� Data: Data is a collection of relevant numerical facts from which conclusions can be drawn.
� Raw data: The numerical data that has been gathered from its original source is called raw data.
It is also termed as primary data.
� Observation: Every individual item in raw data is called an observation.
� Array: The raw data when arranged in ascending or descending order is called an array.
� Frequency: When a particular observation occurs a specific number of times in a given data it is
called its frequency.