Ch 6 Diagrammatic presentation statistics grade 11

Page No 6.29:

Question 1:

From the following data relating to cement production of a factory (2014-19), prepare a simple bar diagram.

Year	2014	2015	2016	2017	2018	2019
Production (in M. Tonnes	125	175	260	310	450	520

ANSWER:

The given data can be presented in the form of a simple bar diagram as follows.

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Question 2:

Average wages of some frirms are given below. Represent this by Simple Bar Diagram.

Firms	A	B	C	D	E
Average Wages (â‚¹)	2,725	3,250	3,750	4,680	5,320

ANSWER:

Simple Bar Diagram

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Question 3:

Present the following data by multiple bar diagram.

Year	B.Com. (H)	Eco. (H)	B. Com.(P)
2017-18	420	200	140
2018-19	320	240	300
2019-20	380	360	480

ANSWER:

Multiple Bar Diagram

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Question 4:

Represent the following data with the help of sub-divided bar diagram:

Year	Production (in '000 tonnes)
Year	Wheat	Rice	Cotton
2017	35	22	10
2018	15	25	16
2019	40	12	20

ANSWER:

Year	Production (in '000 tonnes)			Total
Year	Wheat	Rice	Cotton	Total
2017 2018 2019	35 15 40	22 25 12	10 16 20	67 56 72

Page No 6.29:

Question 5:

Represent the data relating to the cost of production in a factory by means of percentage diagram:

Element of Cost (in '000 tonnes	Items
Element of Cost (in '000 tonnes	A	B	C
Raw Materials	75	55	60
Wages	45	30	25
Factory overheads	15	10	30
Office overheads	5	15	5

ANSWER:

Element of cost	Firm A	Percentage(%) Cost	Firm B	Percentage(%) Cost	Firm C	Percentage(%) Cost
Raw material Wages Factory overhead Office overhead	75 45 15 5	53.57 32.14 10.71 3.58	55 30 10 15	50 27.27 9.09 13.64	60 25 30 5	50.00 20.83 25.00 4.17
Total	140	100	110	100	120	100

Page No 6.30:

Question 6:

From the following data of imports of a firm, prepare a suitable diagram.

Year	2015	2016	2017	2018	2019
Imports (â‚¹ in Lakhs)	16	22	34	170	25

ANSWER:

Broken- Scale Bar Diagram

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Question 7:

Represent the following data relating to net exports of a company by deviation bar diagram.

Year	2014	2015	2016	2017	2018	2019
Net Exports (â‚¹ in Crores)	250	160	(−)80	50	(−)110	70

ANSWER:

Deviation Bar Diagram

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Question 8:

the estimated percentage break-up of the cost of construction of a house (excluding cost of land) is as follows:

Labour	Bricks	Cement	Steel & Timber	Marble	Miscellaneous
20%	12%	25%	15%	13%	15%

Construct a pie diagram to represent the given data.

ANSWER:

The percentage values are converted into degree values using the following formula.
$Degree share = \frac{Percentage share}{100} \times 360 = Percentage share \times 3.6$

Items	Expenditure (in percent)	Degree Share
Labour Bricks Cement Steel and timber Marble Miscellaneous	20 12 25 15 13 15	20 × 3.6 = 72° 12 × 3.6 = 43.2° 25 × 3.6 = 90° 15 × 3.6 = 54° 13 × 3.6 = 46.8° 15 × 3.6 = 54°
		360°

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Question 9:

Draw two pie diagrams to represent the marks obtained by Isha and Utkarsh (out of 50) in an examination.

Subject	Isha	Utkarsh
Maths	40	37
Economics	35	45
Accounts	45	40
Commerce	46	34
English	34	44

ANSWER:

The percentage values are converted into degree values using the following formula.
$Degree share = \frac{Percentage share}{100} \times 360 = Percentage share \times 3.6$

Subject	Marks obtained by Isha	Percentage Value	Degree Share
Maths	40	$\frac{40}{200} \times 100 = 20$	20 × 3.6 = 72°
Economics	35	$\frac{35}{200} \times 100 = 17.5$	17.5 × 3.6 = 63°
Accounts	45	$\frac{45}{200} \times 100 = 22.5$	22.5 × 3.6 = 81°
Commerce	46	$\frac{46}{200} \times 100 = 23$	23 × 3.6 = 82.8°
English	34	$\frac{34}{200} \times 100 = 17$	17 × 3.6 = 61.2°
Total	200		360°

Subject	Marks obtained by Utkarsh	Percentage Value	Degree Share
Maths	37	$\frac{37}{200} \times 100 = 18.5$	18.5 × 3.6 = 66.6°
Economics	45	$\frac{45}{200} \times 100 = 22.5$	22.5 × 3.6 = 81°
Accounts	40	$\frac{40}{200} \times 100 = 20$	20 × 3.6 = 72°
Commerce	34	$\frac{34}{200} \times 100 = 17$	17 × 3.6 = 61.2°
English	44	$\frac{44}{200} \times 100 = 22$	22 × 3.6 = 79.2°
Total	200		360°

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Question 10:

Represent the following data with help of pie diagram.

Items	Rent	Food	Clothing	Transportation	Recreation	Savings	Others
Expenditure (in percent)	20%	25%	22%	15%	8%	6%	4%

ANSWER:

The percentage values are converted into degree values using the following formula.
$Degree share = \frac{Percentage share}{100} \times 360 = Percentage share \times 3.6$

Items	Expenditure (in percent)	Degree Share
Rent Food Clothing Transportation Recreation Savings Others	20 25 22 15 8 6 4	20 × 3.6 = 72 25 × 3.6 = 90 22 × 3.6 = 79.2 15 × 3.6 = 54 8 × 3.6 = 28.8 6 × 3.6 = 21.6 4 × 3.6 = 14.4
Total		360°

Page No 6.31:

Question 11:

The following table gives the number of tyres manufactured by a company for different years.

Year	No. Tyres Produced
2015-16	5,000
2016-17	7,500
2017-18	11,000
2018-19	15,600
2019-20	16,000

Present the data with help of a suitable diagram.

ANSWER:

The given data can be presented in the form of a simple bar diagram as follows.

Page No 6.31:

Question 12:

the following table gives the number of students appearing at the various examination from a college in 2017, 2018 and 2019.

Year	2017	2018	2019
B.A.	250	300	175
B.B.A	425	450	510
B.Com.	175	220	240

Represent the data by a suitable diagram.

ANSWER:

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Question 13:

The following table gives the monthly expenditure of two families A and B. Represent them by means of sub-divided bar diagram and percentage diagram.

Items of Expenditure	Family A (income: â‚¹ 50,000)	Family B (Income: 80,000)
Food	15,000	23,000
Clothing	9,000	17,000
House Rent	11,000	11,000
Education	5,000	9,000
Fuel and Lighting	4,000	13,000
Miscellaneous	6,000	7,000

ANSWER:

Items of Expenditure	Family A (Income: Rs 50,000)	Percentage (%) Expenditure	Family B (Income: Rs 80,000)	Percentage (%) Expenditure
Food Clothing House Rent Education Fuel and Lighting Miscellaneous	15000 9000 11000 5000 4000 6000	$\frac{15000}{50000} \times 100$ = 30 $\frac{9000}{50000} \times 100$ =18 $\frac{11000}{50000} \times 100$ =22 $\frac{5000}{50000} \times 100$ =10 $\frac{4000}{50000} \times 100$ =8 $\frac{6000}{50000} \times 100$ =12	23000 17000 11000 9000 13000 7000	$\frac{23000}{80000} \times 100$ =28.75 $\frac{17000}{80000} \times 100$ =21.25 $\frac{11000}{80000} \times 100$ =13.75 $\frac{9000}{80000} \times 100$ =11.25 $\frac{13000}{80000} \times 100$ =16.25 $\frac{7000}{80000} \times 100$ =8.75
Total	50,000	100	80,000	100

Sub-divided bar Diagram:

Percentage Diagram:

Page No 6.31:

Question 14:

Draw a pie diagram to represent the area of the oceans of world.

Ocean	Pacific	Atlantic	Indian	Antarctic	Arctic
Area (Millions sq. km.	70.8	41.2	28.5	7.6	4.8

ANSWER:

The percentage values are converted into degree values using the following formula.
$Degree share = \frac{Percentage share}{100} \times 360 = Percentage share \times 3.6$

Ocean	Area	Percentage Area	Degree Share
Pacific	70.8	$\frac{70.8}{152.9} \times 100 = 46.30$	46.30 × 3.6 = 166.69
Atlantic	41.2	$\frac{41.2}{152.9} \times 100 = 26.95$	26.95 × 3.6 = 97.02
Indian	28.5	$\frac{28.5}{152.9} \times 100 = 18.64$	18.64 × 3.6 = 67.10
Antarctic	7.6	$\frac{7.6}{152.9} \times 100 = 4.97$	4.97 × 3.6 = 17.89
Arctic	4.8	$\frac{4.8}{152.9} \times 100 = 3.14$	3.14 × 3.6 = 11.304
Total	152.9	100	360°

Page No 6.31:

Question 15:

The following data shows the profits earned by Company A and Company B for the year 2016-17 to 2019-20. Present the data with the help of suitable diagram.

Year	Company A (in â‚¹ '000)	Company B (in â‚¹ '000)
2016-17	225	160
2017-18	310	240
2018-19	450	380
2019-20	575	600

ANSWER:

Page No 6.32:

Question 16:

Represent the following data by Pie diagram.

Items of Expenditure	Family A	Family B	Family C
Food	12,000	30,000	40,000
Clothing	3,500	14,000	10,000
Education	2,000	7,000	3,000
House Rent	1,500	3,000	2,000
Miscellaneous	5,000	6,000	5,000

ANSWER:

For family A

Items of Expenditure	Family A	Percentage expenditure	Degree Share
Food	12000	$\frac{12000}{24000} \times 100 = 50$	50 × 3.6 = 180
Clothing	3500	$\frac{3500}{24000} \times 100 = 14.58$	14.58 × 3.6 = 52.49
Education	2000	$\frac{2000}{24000} \times 100 = 8.33$	8.33 × 3.6 = 29.99
House Rent	1500	$\frac{1500}{24000} \times 100 = 6.25$	6.25 × 3.6 = 22.5
Miscellaneous	5000	$\frac{5000}{24000} \times 100 = 20.84$	20.84 × 3.6 = 70.02

For family B

Items of Expenditure	Family B	Percentage expenditure	Degree Share
Food	30000	$\frac{30000}{60000} \times 100 = 50$	50 × 3.6 = 180
Clothing	14000	$\frac{14000}{60000} \times 100 = 23.33$	23.33 × 3.6 = 83.99
Education	7000	$\frac{7000}{60000} \times 100 = 11.67$	11.67 × 3.6 = 42.01
House Rent	3000	$\frac{3000}{60000} \times 100 = 5$	5 × 3.6 = 18
Miscellaneous	6000	$\frac{6000}{60000} \times 100 = 10$	10 × 3.6 = 36

For family C

Items of Expenditure	Family C	Percentage expenditure	Degree Share
Food	40,000	$\frac{40000}{60000} \times 100 = 66.67$	66.67 × 3.6 = 240.01
Clothing	10,000	$\frac{10000}{60000} \times 100 = 16.67$	16.67 × 3.6 = 60.01
Education	3,000	$\frac{3000}{60000} \times 100 = 5$	5 × 3.6 = 18
House Rent	2,000	$\frac{2000}{60000} \times 100 = 3.33$	3.33 × 3.6 = 11.99
Miscellaneous	5,000	$\frac{5000}{60000} \times 100 = 8.33$	8.3 × 3.6 = 29.99