CAPSULE NOTE
STANDARD 8
MATHEMATICS
(CBSE SYLLABUS)
CHAPTER 5
DATA HANDLING
1
Data:
Data are measurements or observations that are collected as a source of information.
Pictograph:
It is a pictorial representation of data using symbols.
Bar graph:
It is the graphical representation of data using bars of uniform width, their heights being
proportional to the respective values.
Double Bar graph:
A bar graph showing two sets of data simultaneously. It is useful for the comparison of the
data.
DATA HANDLING
2
Circle Graph or Pie- chart:
It is a pictorial representation of the numerical data in a circle form. Here circle is divided
into sectors. The area of each sector is proportional to the magnitude of the data represented
by the sector.
Central angle =
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑚𝑜𝑑𝑒
𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒
× 3600
Note:





In a pie chart a whole circle is divided into sectors.
The central angle of a sector in a pie chart can be more than 1800 .
Sum of all central angles in a pie chart is 3600
In a pie chart two central angles can be of 1800
In a pie chart two or more central angles can be equal.
Example 1:
In a pie chart, the total angle of the centre of the circle is
Solution:
Pie chart is also known as circle graph. The total angle of a circle is 3600 . So In a pie chart,
the total angle of the centre of the circle is 3600
Example 2:
The following pie chart depicts the expenditure of a state government under different heads.
(a) If the total spending is 10 crores, how much money was spent on roads?
(b) How many times is the amount of money spent on education compared to the amount
spent on roads?
(c) What fraction of the total expenditure is spent on both roads and public welfare
together?
DATA HANDLING
3
Solution:
(a) Money spent on roads
= 10% 𝑜𝑓 10 𝑐𝑟𝑜𝑟𝑒𝑠
=
10
100
× 100,000,000 = 10,000,000
(b) Money spent on education = 25% 𝑜𝑓 10 𝑐𝑟𝑜𝑟𝑒𝑠
=
Money spent on road
25
100
× 100,000,000 = 25000000
= 10000000
=
25000000
10000000
= 2.5 𝑡𝑖𝑚𝑒𝑠
(c) Total expenditure
= 100000000
Money spent on both roads and public welfare = 10% + 20% = 30%
=
3𝑐𝑟𝑜𝑟𝑒
10 𝑐𝑟𝑜𝑟𝑒
=
30000000
100000000
=
3
10
Random experiment:
It is an activity which produces some (more than one) well defined outcomes.
Example:
 The experiment of tossing a coin gives two outcomes, head and tail
 Tossing a die gives the outcomes 1,2,3,4,5,6
Event:
An event E for an experiment is the part of the total outcomes of that experiment.
𝑖𝑒: it is the collection of all favorable outcomes.
Eg: On tossing a die, the event of getting an odd number on the die is 1,3,5
If we perform the experiment of tossing a coin twice, the event of getting one head and one
tail is collection of outcomes HT,TH.
DATA HANDLING
4
Sure event:
Sure event is defined as the event always happens.
Eg: Tossing a die.
The outcomes are 1,2,3,4,5,6
Here event is getting even or odd number. We know 1,2,3,4,5,6 are either even or odd. So
event must be happen.
Impossible event
An event which does not occur at all when an experiment is performed.
Eg: Event of getting 7 when tossing a die
There are 6 possibilities. 7 is not possible event. So it is impossible event.
Probability:
Probability is the possibility and impossibility of an event (𝐸)
Probability =
𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 (𝐸 ) + 𝑃 (𝑛𝑜𝑡 𝐸 ) = 1 0 ≤ 𝑃 (𝐸 ) ≤ 1
 Probability of an event can have a value from 0 to 1.
 Probability of sure event is 1.
 Probability of impossible event is 0.
Note:
 Tossing a coin: 2 possibilities (Head and Tail)
 Rolling a die : 6 Outcomes (1,2,3,4,5,6)
Equally likely outcome:
Two or more outcomes are said to be equally likely outcome if each outcome has the same
chance of appearing as any other.
Eg: While we toss a coin, the outcome for getting head and tail are equally likely
𝑖𝑒; While tossing a coin there is equal chance for falling head and tail. So it is equally likely
event
DATA HANDLING
5
Example 3:
Classify the following statements under appropriate headings
(a) Getting the sum of angles of a triangle as 1800 .
(b) India winning a cricket match against Pakistan.
(c) Sun setting in the evening
(d) Getting 7 when die is thrown.
(e) Sun rising from the west
(f) Winning a racing competition by you.
Certain to happen
Impossible to happen
May or may not happen
Solution:
Certain to happen
Getting the sum of angles
of a triangle as 1800 .
Impossible to happen
Getting 7 when die is
thrown.
May or may not happen
India winning a cricket
match against Pakistan.
Sun setting in the evening
Sun rising from the west
Winning a racing
competition by you.
Example 4:
A coin is tossed 200 times and head appeared 120 times. Probability of getting a head in this
experiment is
Solution;
Total number of outcomes
= 200
Favorable outcomes
= 120
Required probability
=
120
200
=
3
5
Example 5:
In a survey of 200 ladies, it has found that 82 like coffee while 118 dislike it. From these
ladies, one is chosen at random. What is the probability that the chosen lady dislike coffee?
Solution:
Total number of outcomes
= 200
Coffee like
= 82
Coffee dislike
= 118
DATA HANDLING
6
Probability of the event
=
=
𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
118
200
=
59
100
Example 6:
A die in rolled once. What is the probability that the number on top will be.
(a) Odd
(b) Less than 1
(c) A factor of 36
(d) A multiple of 3
Solution:
Total number of faces in die
=6
(a) Odd numbers are 1,3,5
Number of favorable outcomes
Required probability
=3
3
1
= =
(b) Less than 1
Number of favorable outcomes
= 0 (no number)
=0
Required probability
(c) Factor of 36
Number of favorable outcomes
Required probability
(d) Multiple of 3
Number of favorable outcomes
Required probability
DATA HANDLING
6
2
0
= =0
6
= 1,2,3,4,6
=5
=
(5 numbers)
5
6
= 3,6
=2
2
1
6
3
= =
( 2 numbers)
7