cbse grade 8 maths

1. Data
Handling
Green House
(by Wasim Ahmed VIII-B9)

2. ALL ABOUT DATA
In various fields, we need information in the of
numerical figures.
Each figure of this kind is called an observation.
The collection of all the observation is called data.
 Some important terms are defined below:-
Data:- A collection of numerical facts regarding a
particular type of information is called data.
Raw data :- A collection of observation gathered initially
is called raw data.

3. TYPES OF GRAPHICAL REPRESENTATION
 Tally chart / frequency chart
 Pictograph
 Bar graph
 Double bar graph
 Histogram
 Pie chart

4. FREQUENCY DISTRIBUTION
Example :- Suppose we make survey of 20 families of a locality and find out
the number of children in each family. Let the observation be.
2,2,3,1,1,2,3,2,2,1,2,2,3,1,2,1,1,3,2,2.
State the frequency of each observation.
Solution:- Arranging the data in ascending order, we get the observation as
1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3.
We find that
1 occurs 6 times;
2 occurs 10 times;
and 3 occurs 4 times;
We say that the frequency of families having 1 child is 6,
the frequency of families having 2 children is 10,
and the frequency of families having 3 children is 4.
Thus, the frequency distribution table of the above data may be
presented as given in the next slide…………

5. FREQUENCY TABLE / TALLY CHAT
No. of
children.
Tally Marks. No. of families
(frequency)
1
2
3
llll l
llll llll
llll
TOTAL
6
10
4
20

6. PICTOGRAPH
A Pictograph represents data using
pictures or symbols.
= 2 Flowers
Month Pictograph
January = 6 Flowers
February = 8 Flowers
March = 4 Flowers

7. 7
BAR GRAPH
A bar graph is a graph that displays
the frequency or numerical
distribution of a categorical
variable, showing values for each
bar next to each other for easy
comparison.

8. 8
BAR GRAPH EXAMPLE
In June 2005, the US Dept of Transportation reported
the following data by observing 1700 motorcyclists
nationwide at randomly selected roadway location:
Proper Helmet 731
Insufficient Helmet 153
No Helmet 816
Total 1,700
Thus, the bar graph of the above data may be
presented as given in the next slide…………

9. 9
Helmets Used by Motorcyclists
731
Source: US Dept of Transportation
153
816
900
800
700
600
500
400
300
200
100
0
Proper Helmet Insufficient Helmet No Helmet
Number of Motorcyclists
Helmet Type
Source: US Dept of Transportation

10. DOUBLE BAR GRAPH EXAMPLE
The table shows the number of pets owned by students
in two classes.
Pet Class A Class B
Dog 12 14
Cat 9 8
Bird 2 3
Represent the information in double bar graph
.

11. 16
12
8
4
0
Thus, the double bar graph of the previous slide data
may be presented as given below
Pet Class A Class B
Dog 12 14
Cat 9 8
Bird 2
3
Dog Cat Bird
Class A Class B

12. HISTOGRAM
A histogram is a bar graph that shows the frequency of data within
equal intervals. There is no space between the bars in a histogram.
Example :The table below shows the number of hours students
watch TV in one week. Make a histogram of the data.
Number of Hours of TV Frequency
1–3 15
4–6 17
7–9 17

13. HISTOGRAM EXAMPLE
Thus, the histogram of the previous slide data may be
presented as given below
Number of Frequency
Hours of TV
1–3
15
4–6 17
7–9 17
20
16
12
8
4
0
Hours of Television Watched
1–3 4–6 7–9
Hours

14. 14
CIRCLE GRAPH/ PIE CHART
A circle graph represents data in a
circular form. A circle graph shows the
relationship between a whole and its
parts. It is divided into sectors. Each
sector visually represents an item in a
data set to match the amount of the
item as a percentage or fraction of the
total data set.

15. HOW TO DRAW A PIE CHART
 Step 1 : Calculate the angle of each sector,
using the formula
 Step 2 : Draw a circle using a pair of
compasses
 Step 3 : Use a protractor to draw the angle
for each sector.
 Step 4 : Label the pie chart and all its
sectors.

16. HOW TO CALCULATE AN ANGLE OF A PIE
CHART
Calculate the angle of each sector, using the
formula
Total angles should add up to 360°

17. PIE CHART EXAMPLE
Example :In a school, there are 750 students in Year1, 420 students
in Year 2 and 630 students in Year 3. Draw a circle graph to
represent the numbers of students in these groups
Solution:
Total number of students = 750 + 420 + 630 = 1,800.
Year 1: size of angle = 750 x 360 =150 degrees
1800
Year 2: size of angle = 420 x 360 = 84 degrees
1800
Year 1: size of angle = 630 x 360 = 126 degrees
1800

18. PIE CHART EXAMPLE
Thus, the pie graph of the previous slide data may be
presented as given below

19. THE MEANING OF PROBABILITY
19
Probability is used to describe RANDOM or CHANCES of events to
occur.
Every day we are faced with probability statements involving the
words:
1. What is the likelihood that X will occur?
2. What is the chance that Brazil will win the 2014 World Cup?

20. 20
EVENT & PROBABILITY
•An event is some specified result that may or may not
occur when an experiment is performed.
•For example, in an experiment of tossing a coin once,
the coin landing with heads facing up is an event, since it
may or may not occur.
•The probability of an event is a measure of the likelihood
of its occurrence.

21. THE EQUAL-LIKELIHOOD MODEL
21
•This model applies when the possible outcomes of an
experiment are equally likely to occur.
•Suppose there are N equally likely possible outcomes from an
experiment.
•Then the probability that a specified events equals the
number of ways, f, that the event can occur, divided by the
total number, N, of possible outcomes.

22. 22
The probability is
f = No. of ways event can occur
N = Total number of possible outcomes.
f
N
In other words, in a situation where several different outcomes are
possible, we define the probability for any particular outcome as a
fraction of the proportion.

23. 23
PROBABILITY EXAMPLE
Example A jar contains 1000 marbles, 800 are black and 200 are red.
What is the probability of drawing a black marble out of the jar.
Solution:
Here 800 is the number of possible outcomes, f
The total number of possible outcomes is 1000, N
Thus the probability is
p(black)   
and
0.8
8
10
800 black marbles
1000 total marbles
0.2
2
p(red)   
10
200 black marbles
1000 total marbles
The probability of drawing a black marble is much higher than the probability of
you picking a red marble because there are more black marbles in the jar.