2. Tabulation
There are 40 children in class 8B of a school. The grades secured
by the students in the mathematics paper during the half yearly
examination is as follows.
A E C B E A B C B
D A B C A D B D E
A D E A B C B E B
A A E C B C B A B
A C C B
i. How many children secured A grade?
ii. How many got B grade ?
iii. How many got below C grade?
iv. What is the grade scored by majority number
of students ?
v. How many children got the least grade ?
To answer the first question , we need to count the grade A only
for the second we count the B grade and the third we need to
count the grades D & E .
What about the fourth one ?
We have to add each type separately ,right ?
Here it is convenient to record this counting first:
3. Grade Number of student
A 10
B 12
C 8
D 4
E 6
Total 40
Now can’t you answer all the questions easily?
Here the table shows A grade repeated 10 times , B grade repeated
12 times and C grade 8 times so on.
The number of repetitions (or occurrences) is known
as frequency.
Now consider another
problem.
The temperatures (in degree
Celsius) of a particular town
in a month are listed below :
Statistics is a branch of
science which deals with
data collected for specific
purposes .We can make
decisions about the data by
analyzing & interpreting it
4. 26 29 27 26 29 30 31 30
28 26 27 31 28 31 27 28
29 30 26 28 30 30 29 28
27 30 28 27 27 28
i. How many days have temperature as 26 ̊C ?
ii. How many days have temperature below 28 ̊C ?
iii. How many days have temperature as 30 ̊C ?
iv. How many days have temperature in between 29 &
31 ̊C ?
v. Which temperature occurs the most ?
To answer the first question , we need to count the temperature
26 ̊C only, for the second we count the temperatures 26 &27 ̊C .
And for the third question ,
count 30 ̊C only .
What about the fourth question ?
For convenient first record this counting :
5. Temperature
(in degree
Celsius )
Tally Number of
repetitions
26 IIII 4
27 IIII I 6
28 IIII II 7
29 IIII 4
30 IIII I 6
31 III 3
Total 30
Lets make a table , we must note how many times each
temperature occurs .The lowest temperature is 26 ̊C and the
highest is 31 ̊C .
Write the numbers from 26 to 31 in a column and check how
many times each is repeated . We can use method of tallies .
Now it is easy to answer all questions above , just by looking t
the table is n’t it ?
This table shows how many times each temperature occurs ,such
as 26 four times ,27 six times ,28 seven times so on .In tables of
this kind ,the number of occurrences is generally called frequency.
6. A table shows counts for a variable is called a
frequency table .
1) The height of the 10 th standard students are
listed below .(height is in centimeters) .
130 138 130 136 135 134
134 13 1 13 0 138 137 135
133 123 132 136 138 134
130 136 137 130 135 134
130 131 133 135 132
Make a frequency table and answer these questions :
i. How many students have height
of 135 cm ?
ii. How many students have height
below 136 cm ?
iii. How many students have height
of 137 & 138 cm ?
iv. Which height occurs the most ?
v. Which height occurs the least ?
The sores obtained by the students in a
class are listed below . Make a
frequency table and answer the following
questions :
2
)
“Statistics may rightly
called the science of
averages” –A.L BOWLEY
7. 10 8 4 5 6 9 7
6 5 9 10 8 8 9
7 6 3 2 10 9 9
7 8 6 5 4 7 7
6 3
i. How many children got above 8 ?
ii. How many scored 7 marks ?
iii. How many children got 10 ?
iv. How many scored in between 5 to 9 ?
3) The daily wages of labors in a factory are listed
below ( in rupees) .
110 115 120 115 110
120 110 120 115 125
125 115 120 110 120
Make a frequency table and answer these questions :
i. How many of them have salary RS 115 ?
ii. How many of them have highest salaries ?
iii. How many of them got least salary RS 110 ?
iv. How many of them have salary RS 115 ?
v. How many labors are working in that factory ?
8. Here the lowest score is 1 & the highest is 69 .
Another form
The total marks of an exam is 100.Following represents the
marks obtained by the student.
69 55 1 17 35 56 22 48 67
46 33 45 53 68 32 48 49 38
47 58 52 54 55 47 39 28 56
59 46 5 36 57 66 43 55 37
4 1 27 16 11 31 40 61 21 51
55 20 52 48
To make a table as we did so far,
we would have to write all
numbers from 1 to 100 .But all
such numbers are not really
needed .More over from such
table , we don't get a general
idea of the score obtained by
the students . so we do it in a
slightly different way to find the
frequency table .Instead of
writing the actual scores in a
column , we need to classify
them as groups .
That is ,
Below 10
10 to 20 (20 is not included)
20 to 30 (30 is not included)
30 to 40 (40 is not included)
40 to 50 (50 is not included)
The frequency of a
particular data value is the
number of times the data
value occurs. The frequency
of a data value is often
denoted by “f ” . A
frequency table is
constructed by arranging
collected data values in
ascending order of
magnitude with their
corresponding frequencies .
9. s
50 to 60 (60 is not included)
60 to 70 (70 is not included)
For convenient we can write
0 - 10
10 -20
20 -30
30 -40
40 - 50
……….. So on
Each group is known as class.
The scores included in the 0 - 10 is the scores
Below 10 .
What about in the second class. ?
The scores 10 & above 10 but below 20 .
Similarly what about other classes ?
In the class 0 - 10 , 0 is the lower limit & 10 is the
Upper limit .
Here we are excluded the upper limit values & lower
limit values are included .Such classes are called
exclusive classes .
Then what about the differences ?
The difference between upper limit values &
lower limit values is known as class interval.
When the set of data value are
spread out ,it is difficult to set
up a frequency table for every
data value as there will be too
many rows in the table .So we
group the data in to class
intervals (or groups) to help us
organize , interpret & analyze
the data . Each group starts at
data value data value that is a
multiple of that group.
For eg , if the size of the
group is 5 ,then the groups
should start at 5,10, 15,20, etc.
10. That is , above class interval is 10 .
Now we need to count the scores in each class .
Class Tally frequency
0 -10 II 2
10-20 III 3
20 -30 IIII 5
30-40 IIII IIII 9
40-50 IIII IIII II 12
50-60 IIII IIII IIII 14
60-70 IIII 5
Total 50
Now we can easily answer the following
questions :
i. Which is the highest frequency ?
ii. Which is the lowest frequency ?
iii. How many of them got scores less
than 20 ?
iv. How many of them got scores less
than 20 ?
v. How many of them got scores in
between 40 & 50 ?
Range is the
difference between
upper limit & lower
limit values . That
is , R=U-L
The mid point of
the class interval is
known as the class
mark . That is ,
R=(U+L)/2
11. Height(in centimeter) of some people are listed below:
Now consider another problem .
150 100 149 160
109 108 112 119
120 115 129 130
142 145 148 156
162 189 185 145
120 129 130 188
189 142 100 160
109 150 145 148
156 129 130 112
Now we can
make a frequency
table by choosing
the class interval
as follows :
Any statistical study starts
with a process data
collection. The second
process is the a of the
collected data . we can
presented the collected data
in numerical as well as
graphical presentation.
collected data can be
numerically presented in
three ways .they are row
data , discrete continuous
frequency distribution.
12. Here in all the class intervals we include the upper limit also
.That is , the classes in which both upper limit & lower limit
values can be included in the same class are called inclusive
classes .
Height Tally Number
100 -109 IIII 5
110-119 IIII 4
120 -129 …………… ……………
130-139 …………… ……………
140-149 …………… ……………
150-159 …………… ……………
160-169 …………… ……………
170-179 …………… ……………
180-189 …………… ……………
190-199 …………… ……………
Total 36
13. 1) The Weight (in kilograms) of the
members of the school health club are
given below
37 40 59 35 ⅟2
26 ⅟2 52 36 ⅟2 40
⅟2
35 ⅟2 59 37 ⅟2 46
55 36 ⅟2 40 ⅟2 35
⅟2
26 ⅟2 52 40 33
44 ⅟2 40 26 ⅟2 53
55 37 44 ⅟2 35 ⅟2
We want to make a frequency
table .
would classes like 30 -34 , 35- 39
,40-44, 45-49 &
so on do ?
In which class would we put 44
⅟2 Kg ?
For eg ,
we can take classes as 30 -35 , 35 -
40 ,
40-45 ,so on.
On 44 ⅟2 can be put in the class
40-45 .
That is , here we need exclusive
classes .
Now we can make a frequency
table.
Discrete frequency distribution
is a table of 2 columns in which
the first is variable values in
individual form & second is the
frequency. It is known as discrete
frequency table .
Continuous frequency
distribution is a table of 2
columns in which the first is
variable values in class form &
second is the frequency.
14. in
class Tally Frequency
30-35 …………… ……………
35-40 …………… ……………
40-45 …………… ……………
45-50 …………… ……………
50-55 …………… ……………
55- 60 …………… ……………
Total ……………
1) Given below are the scores of the children in class 9B .Make
a frequency table ?
23 25 38 47 40 39 26
31 37 32 41 30 25 38
33 23 47 40 39 31 40
36 25 47 41 40 47 26
33 29 32
15. We have seen how numerical data can be pictorially represented
as bar charts .
A new picture
Now let’s see how the data in a frequency table can be
represented by a picture .
The table below gives wages of labors.
wages Number of
labors
(frequency)
100 -120 5
120-140 11
140 -160 16
160-180 20
180-200 9
200-220 2
Total 63
See how this data is represented by a picture .
Data can be
graphically
presented in many
ways . Commonly
used methods are.
Histogram,
polygon
,pictogram ,
pie diagram ,bar
diagram , ogive
curves , etc.
16. Draw a horizontal & vertical line.
Step 1
The classes are marked on the horizontal line& frequencies
on the vertical line .
Step 2
Step 3
Draw a rectangle for each class .
Step 4
Then shade the rectangle.
5
11
16
20
9
2
0
5
10
15
20
25
100-120 120-140 140-160 160-180 180-200 200-220
frequencies
classes
Histogram
frequencies
17. The width of each rectangle shows
the length of the class interval &
its height shows the frequency .
Such a picture is called a Histogram .
1) Details of rain fall in June & July are given in the table
below . Draw a Histogram .
Rain fall(mm) Days
10-20 4
20-3 0 2
30-40 14
40-50 12
50-60 15
60- 70 10
70-80 6
80-90 15
90-100 18
2) Details of weights are given in the table below . Draw a
Histogram .
18. Weight(kg) Number of children
35-37 3
37-39 6
39-41 9
41-43 12
43-45 15
45- 47 8
47-49 5
2) Details of ages are given in the table below . Draw a
Histogram .
Age Number
20-30 2
30-40 4
40-50 8
50-60 7
60-70 12
70- 80 2
80-90 3
Total 38
19. LOOKING BACK
Learning outcomes What I can With
teachers help
Must
improve
Making a frequency
distribution of individual
entries from given data
Dividing given data in to
classes & make a
frequency table .
Explaining the need for
grouping in to classes in
making a frequency table
.
Representing a frequency
table as a histogram .
