Data
The pieces
of information collected for some purpose are called data.
The data is also defined as the collection of facts and figures.
Raw Data
The data
originally collected, observed or received are usually unorganized in nature
and is called raw data. After the collection of raw data, it is organized and
put in the form of a table.
We cannot find any useful information easily from the raw data. To reach on any conclusion, we organize raw data in form of tables and graphs.
Range
The
difference between the highest and the lowest value of the variable in a set of
data is called the range.
For example: The runs scored by a cricket player in 10 matches is as follows:
34 56 12 75 23 38 10 18 95 25
Lowest value: 10
Highest value: 95
Range = Highest value - Lowest value
= 95 - 10 = 85
Arranged Data
The data may
be arranged in ascending or descending order. This arrangement of data is
called arranged or arrayed data.
Frequency
Frequency of
a value is the number of times it occurs in a given data set. Data can be
presented with the help of a table called frequency distribution table. There
are two types of frequency distribution table:
1. Ungrouped
frequency distribution table
2. Grouped
frequency distribution table
Ungrouped Frequency Distribution Table
It is the
tabular representation of the frequency of each individual piece of data.
Consider the following example:
Example: The marks obtained by 20 students in
a test (out of 40) are given below:
38 32 39 35 36 31 37 35 32 33 36 35 33 34 33 32 32 31 34 31
We arrange
them in ascending order as follows:
31 31 31 32 32 32 32 33 33 33 34 34 35 35 35 36 36 37 38 39
From above,
we can see that 31 marks are obtained by 3 students whereas 34 marks are
obtained by 2 students. Thus, 3 and 2 are respectively the frequencies of 31
and 34. Similarly, we can find the frequencies of the other values of the
variable and arrange them in a tabular form having two columns.
The
frequency distribution table is prepared by moving systematically down the
column of numbers given and marking tally marks ( l ) in the tally column
against the appropriate group. The tally marks are in groups of 5 which makes
it easy for us to count. We then count the tally marks and write the total in
the frequency column. To check, we add the numbers in the frequency column. The
total should be equal to the total number of observations (in this case 20).
|
Marks
|
Tally marks
|
Frequency
|
|
31
|
lll
|
3
|
|
32
|
llll
|
4
|
|
33
|
lll
|
3
|
|
34
|
ll
|
2
|
|
35
|
lll
|
3
|
|
36
|
ll
|
2
|
|
37
|
l
|
1
|
|
38
|
l
|
1
|
|
39
|
l
|
1
|
|
Total
|
|
20
|
Such a table
is called ungrouped frequency distribution table.
Grouped Frequency Distribution Table
Another way
of organizing raw data is in form of a grouped frequency distribution table. Here,
the heights (cm) of 72 students are given. We can group the data into classes
or categories by writing down the number of students who fall into each class.
Consider the
data,
147 143 148
134 146 156
139 144 148 135
136 152 148
149 142 136
136 150 132 148
142 159 149
135 139 137
152 143 162
159 146 152 142 149 145 149
129 149 139
148 149 141
142 154 149
145 142 151 146 142 152 134
141 137 136
142 148 149 149
133
157 152 148
137 153 146 148
153 139 131 153 148
First
arrange this data in ascending or descending order.
Class Intervals
We will make
groups such as 125–130, 130–135, etc. which are called classes or class
intervals.
Lower class limit and upper class limit
In the
interval 125–130, 125 is called the lower class limit and 130 is called the
upper class limit.
Width of the class
The
difference between the upper class limit and lower class limit is called the
size or width of the class. Here, the class width is 5.
In the
table, it would seem that a number such as 135 would fall in two classes viz.
130–135 and 135–140. However, by convention, 135 is included in the class
135–140. Similarly, a number like 150 would be included in the class 150–155.
