X - Maths - Statistics Part II by Ednexa

1. Statistics – II
Pictorial representation of statistical data
We know that, the classification of numerical
data and frequency tables help us to present
raw data in compact and systematic form which
can be easily understood.
There is another way of presenting the data in
the form of diagrams and graphs which have
visual appeal. These pictorial representations
are easier to follows and eye catching and so
leave an impact on our mind.

2. There are two such methods of representing
numerical data.
1. Diagrammatic representation :
a. Bar Diagram
b. Pie diagram
2. Graphical representation.
a. Histogram
b. Frequency Polygon
c. Frequency Curve

3. Pie Diagram
In this diagram, a circle is drawn and the values
of given items or components are represented
by sectors of this circle.
In fig. O is the centre of the circle and segments
OA and OB are the radii.
∠AOB is the central angle and shaded region
OAB is a sector of the circle.

4. Construction of pie diagram
Step 1:
Using the face that the total of all values of
items or components corresponds to 360°,
we
find
the
central
angle
for
each
component. We use the following formula.

5. Central angle,  
Value of the component
 360
Total values of all the components
Step 2:
We draw a circle of convenient radius. The
circle is divided into a number of sectors to
represent the various items or components.
In order words, the number of sectors is
equal to the number of components.
Exercise 1
1. The following data gives the number of
students using different modes of transport.
Modes of
Bicycle Bus Walk Train Car

6. transport
No. of
140
100 70
40
10
students
Represents the above data using a pie
diagram.
Sol :
We first calculate the central angle for each
item (or component) as shown in the
following table.
Mode
of No. of students
transport
Measure of
central angle
Bicycle
140
140
 360  140
360
Bus
100
100
 360  100
360
Walk
70
70
 360  70
360

7. Train
40
40
 360  40
360
Car
10
10
 360  10
360
Total
360
360°
The pie diagram is shown in figure.

8. 2. Area under different crops in a certain
village is given below. Represents it by a pie
diagram.
Crop
Jowar Wheat Sugarcane Vegetables
Area
8000
6000
2000
2000
(in
hectares)
Sol :
We first evaluate the central angle for each
component as shown in the following table.
Crop
Area
(in Measure of
hectares)
central angle
Jowar
8000
8000
 360  160
18000
Wheat
6000
6000
 360  120
18000
Sugarcane
2000
2000
 360  40
18000
Vegetables
2000
2000
 360  40
18000
Total
18000
= 360°

9. The pie diagram is shown in figure.

10. 3. The following table gives information about
the monetary investment by some residents
in a city.
Mode of
Shares Mutual Real
Investment
Percentage
Gold Government
Funds Estate
10
20
35
Bonds
30
5
of residents
Draw a pie diagram to represent the data.

11. Sol :
We first calculate the central angle for each
item as shown in the following table.
Mode of
Percentage
Investment
Measure of
central angle
Shares
10
10
 360  36
100
Mutual Funds
20
20
 360  72
100
Real Estate
35
35
 360  126
100
Gold
30
30
 360  108
100
Government
5
5
 360  18
100
100
= 360°
Bonds
Total
The Pie diagram is shown in figure.

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