This document discusses data, how it can be organized and represented visually. It provides definitions of key terms like data, raw data, and grouped data. It also describes various visual representations of data like bar graphs, pie charts, and histograms. These visual representations make data easier to understand, compare and analyze. The document also discusses how raw data can be organized and grouped into frequency distribution tables for clearer interpretation.

2. Data is a collection of observations. Visual representation of
data will help us to understand it better and remember the
facts easily.
The word ‘data’ means collection of information in the form
of numerical figures, or a set of given facts.
Examples:
The marks obtained by 10 students of a class in a test are:
76, 83, 95, 100, 56, 32, 80, 67, 75, 46
When some information is collected and presented randomly,
then it is called raw data. A data classified into groups is
called grouped data.
Data in raw form can be represented in the form of pictures
and diagrams. It makes the given data attractive to the
observer. Also, it is easy to understand and to compare it
with other information.

6. Some commonly used diagrams to represent numerical data
are:
Pictographs
Bar graph
Double bar graph
Pie-diagrams or Pie-charts
 Pictographs represent data through appropriate
pictures. In pictographs, the same type of symbol or
picture is used to represent the data. Each symbol is
used to represent a certain value, and this is mentioned
clearly in the graph

7. A representation of data with the help of bars or rectangles in a
diagram is called a bar graph or a bar diagram.
Here, each bar represents only one value of the data, and hence, there
are as many bars as the number of values in the data. The length or
height of a bar indicates the value of the item. The width of a bar and
the gap between the bars is kept uniform to make the diagram look
neat.
VII VIII IX X
2013 139 144 130 120
2010 124 130 105 100
2005 94 99 84 74
0
50
100
150
200
250
300
350
400
Populationofstudents
STUDENTS POPULATION IN SCHOOL

9. Q: The number of hours for which students of a particular class
watched television during holidays is shown through the given graph.
Answer the following.
1. For how many hours did the maximum number of students watch
TV?2. How many students watched TV for less than 4 hours?
3. How many students spent more than 5 hours in watching TV?
1 HOUR 2 HOUR 3 HOUR 4 HOUR 5 HOUR 6 HOUR
Series 1 4 8 22 32 8 6
0
5
10
15
20
25
30
35
Numberofstudents->

10. Sometimes, organizing data becomes a tedious process. In such cases,
we group the raw data. We write the groups as intervals. Each group is
called a class interval. The class interval will have a lower class limit
and an upper class limit.
The difference between the upper class limit and the lower class limit
is called the width or size of the class interval. The number of times a
particular item appears within a particular class interval is called
frequency.
The span of a class interval is called the width or size of the class
interval.
We fill up the rows with tally marks and will count the total number of
tally marks in each group. The number of tally marks in each group is
listed in the frequency column. The completed table is called the
frequency distribution table. With the data in a table, we can draw a
graph.

11. A graph showing two sets of data simultaneously is called a
double bar graph. It is useful for comparing two sets of
data.The length or height of a bar indicates the value of the
item. The width of a bar and the gap between the bars is
kept uniform to make the diagram look neat.
MATHS SCIENCE ENGLISH HINDI
2005-06 30 50 40 35
2010-11 60 45 55 60
0
10
20
30
40
50
60
70
MARKS OBTAINED BY STUDENTS

12. 40%
17%
11%
32%
CHILDREN SPEND THEIR EVENING
watching TV
PLAYING
HOMEWORK
studying
A pie diagram or a pie chart is a circle
divided into several sectors. The circle
represents the total value of the given data,
and the sectors represent the proportion of
the components of the total.

13. Q: Adjoining pie chart gives the expenditure (in percentage) on various
items and savings of a family during a month.
(i) On which item, the expenditure was maximum?
22%
36%7%
14%
21%
Saving of money by a family
Education for
children
Food
Transport
Cloth
(ii) Expenditure on which item is equal to the total savings of the
family?
Answer the following.

14. If we make a frequency distribution table for each observation, then
the table would be too long, so, for convenience, we make groups of
observations say, 0-10, 10-20 and so on, and obtain a frequency
distribution of the number of observations falling in each group
Data presented in this manner is said to be grouped and the
distribution obtained is called grouped frequency distribution.

15. WHATHAVEWE learn ?
 1. Data mostly available to us in an unorganized form is called raw
data.
 2. In order to draw meaningful inferences from any data, we need to organize
the
data systematically.
 3. Frequency gives the number of times that a particular entry
occurs.
 4. Raw data can be ‘grouped’ and presented systematically through
‘grouped
frequency distribution’.
 5. Grouped data can be presented using histogram. Histogram is a type
of bar diagram, where the class intervals are shown on the horizontal
axis and the heights of the bars show the frequency of the class
interval. Also, there is no gap between the bars as there is no gap
between the class intervals. 6. Data can also presented using circle graph or pie chart . A circle
graph shows the relationship between a whole and its part.
 7. There are certain experiments whose outcomes have an equal
chance of occurring.

16.  8. A random experiment is one whose outcome cannot be predicted
exactly in advance.
 9. Outcomes of an experiment are equally likely if each has the
same chance of occurring.
 1o. One or more outcomes of an experiment make an event.
 11. Chances and probability are related to real life.