T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 6 - Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 6 – Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams is regarded as an important concept to be studied thoroughly by the students. Here, we have provided T.R. Jain and V.K. Ohri Solutions for Class 11.

Board

CBSE

Class

Class 11

Subject

Statistics for Economics

Chapter

Chapter 6

Chapter Name

Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams

Number of questions solved

05

Category

T.R. Jain and V.K. Ohri

Chapter 6 – Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams cover below-mentioned concepts

  • What is a bar diagram?
  • Types of bar diagram
  • Pie or Circular Diagrams
  • Multiple bar diagram

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 6 – Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams

Question 1

Represent the following data by a percentage bar diagram.

Subjects

Number of Students

2016-17

2017-18

Statistics

25

30

Economics

40

42

History

35

28

Solution

Subject

2016-17

2017-18

Number of students (%)

Cumulative Percentage

Number of students (%)

Cumulative Percentage

Statistics

25

25

30

30

Economics

40

60

42

72

History

35

100

28

100

Total

100

100

Percentage Bar Diagram

Question 2

Draw a suitable diagram to represent the following information

Factory

Selling price per unit (in ₹)

Quantity Sold

Cost Components (in ₹)

Wages

Material

Miscellaneous

Total

X

400

20

3,200

2,400

1,600

7,200

Y

600

30

6,000

6,000

9,000

21,000

Also, show profit and loss.

Solution

First of all, we shall calculate the cost (wages, materials, miscellaneous) and profit per unit as given in the following table.

Factory X (20 units)

Factory Y (30 units)

Total Cost (₹)

Per Unit Cost (₹)

Total Cost (₹)

Per Unit Cost (₹)

Wages

3,200

160

6,000

200

Materials

2,400

120

6,000

200

Miscellaneous

1,600

80

9,000

300

Profit/Loss

800

(8,000-7,200)

40

-3,000

(18,000-21,000)

-100

Note: (Negative profit is regarded as a loss)

An appropriate diagram for representing this data would be the rectangle whose widths are in the ratio of the quantities sold, i.e, 20:30, i.e, 2:3. Selling prices would be represented by the corresponding heights of the rectangles with various costs (wages, materials, miscellaneous) and profit or loss represented by the various divisions of the rectangles as shown in the diagram given on the next page.

Sub-Divided Bar Diagram

(Note: In the case of profit, i.e., when selling price > cost price, the entire rectangle will lie above the X-axis. But in case of loss, we will have a rectangle with a portion lying below the X-axis which will reflect the loss incurred, it cannot be recovered through sales)

Question 3

Following are the data about the market share of four brands of TV sets sold in Panipat and Ambala. Present the data in the pie chart.

Brand of Sets

Units sold in Panipat

Units sold in Ambala

Samsung

480

625

Akai

360

500

Onida

240

438

Sony

120

312

Solution

Total sets sold in Place A and Place B are 1,200 and 1,875 respectively. Data are to be represented by two circles whose radii are in the ratio of square roots of total TV sets sold in each city in the ratio of : or 1:1. The calculations regarding the construction of the pie diagram are as follows.

Brands of Sets

Place A

Place B

Sets Sold

Sales(₹)

Sales in terms of components of 360°

Sets Sold

Sales %

Sales in terms of components of 360°

Samsung

480

40

\(\frac{40}{100}\, \times \, 360^{\circ}\, =\, 144^{\circ}\)

625

33.3

\(\frac{33.3}{100}\, \times \, 360^{\circ}\, =\, 119.88^{\circ}\)

Akai

360

30

\(\frac{30}{100}\, \times \, 360^{\circ}\, =\, 108^{\circ}\)

500

26.7

\(\frac{26.7}{100}\, \times \, 360^{\circ}\, =\, 96.12^{\circ}\)

Onida

240

20

\(\frac{20}{100}\, \times \, 360^{\circ}\, =\, 72^{\circ}\)

438

\(\frac{23.4}{100}\, \times \, 360^{\circ}\, =\, 84.24^{\circ}\)

Sony

120

10

\(\frac{10}{100}\, \times \, 360^{\circ}\, =\, 36^{\circ}\)

312

16.6

\(\frac{16.6}{100}\, \times \, 360^{\circ}\, =\, 59.76^{\circ}\)

Total

1,200

360°

1,875

360°

Pie Diagram

Question 4

The following table shows the interest of students in a school in different games.

Games

Table Tennie

Volleyball

Hockey

Basketball

Cricket

No of Students

500

300

350

400

550

Solution

Simple Bar Diagram

Question 5

The following table shows the monthly expenditure of different families on different items.

Items of Expenditure

Education

Clothing

Food

Rent

Other

Total Expenditure

Family A

1,500

1,000

1,250

750

500

5,000

Family B

1,700

850

1,200

850

600

5,200

Family C

1,600

700

1,500

800

600

5,200

Represent the data in the form of a sub-divided bar diagram.

Solution

Sub-Divided Bar Diagram

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