Representation of Data - Practice Questions & MCQ

Representation of Data

Any bit of information that is expressed as a numerical number is data. For example, the marks you obtained in your Math exam are data. Data is a collection of information, measurements or observations. 

The data once collected must be arranged or organised in a way so that inferences or conclusions can be made out from it.

The following are the ways to represent data

1. Ungrouped distribution
2. Ungrouped frequency distribution
3. Grouped frequency distribution

The frequency of any value is the number of times that value appears in a data set. 

Ungrouped distribution

Consider the marks obtained (out of 100 marks) by 30 students of Class XI of a school:

$
\begin{array}{llllllllll}
10 & 20 & 36 & 92 & 95 & 40 & 50 & 56 & 60 & 70 \\
92 & 88 & 80 & 70 & 72 & 70 & 36 & 40 & 36 & 40 \\
92 & 40 & 50 & 50 & 56 & 60 & 70 & 60 & 60 & 88
\end{array}
$

This representation is called Ungrouped distribution, as all the values are simply mentioned and separated by a comma.

Ungrouped Frequency Distribution

Observe that, 4 students got 70 marks. So the frequency of 70 marks is 4.

To make the data more easily understandable, we create a table,

$
\begin{array}{|c|c|}
\hline \text { Marks } & \text { Number of students } \\
\hline 10 & 1 \\
20 & 1 \\
36 & 3 \\
40 & 4 \\
50 & 3 \\
56 & 2 \\
60 & 4 \\
70 & 4 \\
72 & 1 \\
80 & 1 \\
98 & 2 \\
92 & 3 \\
95 & 1 \\
\hline \text { Total } & \mathbf{3 0} \\
\hline
\end{array}
$

The above table is called a Ungrouped Frequency Distribution.

Grouped Frequency Distribution

We can show data as ranges of marks and the number of students that obtained marks in that range.

So we can represent this data as

$
\begin{array}{|l|c|c|c|c|c|c|}
\hline \text { Class interval } & 10-25 & 25-40 & 40-55 & 55-70 & 70-85 & 85-100 \\
\hline \text { Number of students } & 2 & 3 & 7 & 6 & 6 & 6 \\
\hline
\end{array}
$

Here we have taken groups (range) of marks. This is why it is called Grouped distribution.

Also, the difference of marks in each interval is $15(25-10=15,70-55=15, \ldots)$. This number is called the width of the class interval. Here width is 15, but we can take any width as per our convenience.

The above table is called a Grouped frequency distribution.