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RD Sharma Solutions Class 9 Graphical Representation Of Statistical Data Exercise23.1

RD Sharma Solutions Class 9 Chapter 23 Exercise 23.1

Q1: The following table shows the daily production o f T.V. sets in an industry for 7 days o f a week.

Represent the above information by a pictograph.

Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Number of tv sets

300 400 150 250 100 350 200

Answer

The given information can be represented using a pictograph in the following manner:

Day Number o f T.V. Sets

M o n d ay

T uesd ay

W ed n esd ay HllT h u rsd ay ■■111

F rid ay 11S a tu rd ay m m i ,S u n d ay ■■■■

50T.V Sets

Q2: The following table shows the number o f Maruti cars sold by five dealers in a particular month:

Represent the above information by a pictograph.

Dealer saya Bagga links D.D Motors Bhasin Motors

Cars sold 60 40 20 15

Competent

10

Answer

The given information can be represented using a pictograph in the following manner:

P f s le r N um ber M a ro ti C ars SoM

£nya f tn jr u H u n , f i - i a . 6 _ 1 & ,

Rflggj Link* 'C U a- Sl-O- 8LJ&.. OLSJ.D-D. Muiorti f i ' in . H ' n .

Bhasin Motors

Competent -ecaa-* 1C can

Q 3: The population o f Delhi State in different census years is as given below:

Census year 1961 1971 1981 1991 2001

Population in Lakhs 30 55 70 110 150

Represent the above information with the help of a bar graph.

Answer

While drawing a bar graph, we keep in mind that:

1. The width of the bars should be uniform throughout.2 The gap between any two bars should be uniform throughout.3. Bars may be either horizontal or vertical.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the population in lakhs respectively. We have to draw 5 bars of different heights given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles o f the same width at these points. The heights of the rectangles are proportional to the population in lakhs. The vertical bar graph of the given data is following:

Note that each bar is of the same width and the gap between them is uniform. Make sure that the width o f the bars and the gap between them should not be necessarily same.

Q4: Read the bar graph shown in the figure and answer the following questions:

(i) What is the information given by the bar graph?

(ii) How many tickets o f Assam State Lottery were sold by the agent?

(ill) Of which state, were the maximum number o f tickets sold?

(iv) State whether true or false.

The maximum number o f tickets sold is three tim es the minimum number o f tickets sold.

(v) Of which state were the minimum numbers o f tickets sold?

Ans:

(1) The bar graph represents the number o f tickets of different state lotteries sold by an agent on a day.

(2) The number o f tickets of Assam State Lottery were sold by the agent is 40.

(3) The maximum numbers o f tickets were sold is 100, in the state Haryana

(4) The maximum number o f tickets were sold is 100, in the state Haryana the minimum number o f tickets were sold is 20, in the state Rajasthan. It is clear that 100 are equal to the 5 times of 20. Hence, the statement is false.

(5) The minimum numbers of tickets were sold is 20, in the state Rajasthan.

Q5: Study the bar graph representing the number o f persons in various age groups in a town shown in figure Observe the bar graph and answer the following questions:

(i) What is the percentage of the youngest age-group persons over those in the oldest age group?

(ii) What is the total population o f the town?

(iii) What is the number o f persons in the age-group 60-65?

(iv) How many persons are more in the age-group 10-15 than in the age group 30-35?

(v) What is the age-group o f exactly 1200 persons living in the town?

(vi) What is the total number o f persons living in the town in the age-group 50-55?

(vii) What is the total number o f persons living in the town in the age-groups 10-15 and 60-65?

(vii) Whether the population in general increases, decreases or remains constant with the increase in the age-group.

Ans:

(1) The youngest age-group is 10-15 years. The number of persons belonging to this group is 1400. The oldest age-group is 70-75 years. The number of persons belonging to this group is 300. The percentage of youngest age-group persons over those in the oldest group is

W x l 0 °_ 1400 " 3

= 466-| X

(2) The population of the town is 300+ 800+900+1000 +1100 +1200+1400 = 6700

(3) The number o f persons in the age group 60 - 65 is 800.

(4) The number o f persons in the age group 10 - 15 is 1400 and the number of persons in the age group 30-35 is 1100. Hence the number of more persons in the age group 10 - 15 than the group 30-35 is 1400 — 1100 = 300.

(5) The age group of 1200 persons living in the town is 20 - 25.

(6) The total number o f persons living in the town in the age-group 50 - 55 is 900.

(7) The total number o f persons living in the town in the age-groups 10-15 and 60 - 65 is 1400 + 800 = 2200.

(8) It is shown from the bar graph that the height o f the bars decreases as the age-group increases. Hence, the population decreases with the increases in the age-group.

Q6: Read the bar graph shown in the figure and answer the following questions:


(ii) What was the number o f commercial banks in 1977?

(iii) What is the ratio o f the number o f commercial banks in 1969 to that in 1980?

(iv) State whether true or false:

The number o f commercial banks in 1983 is less than double the number o f commercial banks in 1969.

Ans:

(1) The bar graph represents the number o f commercial banks in India during some particular years.

(2) The number o f commercial banks in 1977 was

120 + (140 - 120)/2

=> = 120+ 20 /2

=> = 120 + 10


80+ (1 0 0 -8 0 ) /2

=> = 80 + 20/2

=> = 80 + 10

=> = 90

The number o f commercial banks in 1980 was

140+ (160-140)/2

=> = 140 +20/2

=> =140+10

= 150

Hence, the required ratio is 90/150

=> 3/5

= >3 : 5


220 + (240-220)/ 2

= > = 220 + 20/2

= > = 220 +10

=>130

=> = 230

The number o f commercial banks in 1969 was 90.

When we multiply this number by 2, it becomes 2 x 90 =180

Clearly, 230 is not less than 180. Hence the statement is false.

Q7: Given below is the bar graph indicating the marks obtained out o f 50 in mathem atics paper by 100 students. Read the bar graph and answer the following questions.

i) It is decided to distribute workbooks on mathem atics to the students obtaining less than 20 marks, giving one workbook to each o f such

students. If a workbook costs Rs. 5, what sum is required to buy the workbooks?

(ii) Every student belonging to the highest m ark group is entitled to get a prize o f Rs. 10. How much amount o f money is required for distributing

the prize money?

(iii) Every student belonging to the lowest mark-group has to solve 5 problems per day. How many problems, in all, will be solved by the students

o f this group per day?

(iv) State whether true or false.

(a) 17% students have obtained marks ranging from 40 to 49.

(b) 59 students have obtained marks ranging from 10 to 29.

(v) What is the number o f students getting less than 20 marks?

(vi) What is the number o f students getting more than 29 marks?

(vii) What is the number o f students getting marks between 9 and 40?

(viii) W hat is the number o f students belonging to the highest m ark group?

(ix) What is the number of students obtaining more than 19 marks?

Ans:

(1) The number o f students obtaining less than 20 marks is 27 + 12 = 39

Hence, the total cost to buy the work books is 5 x 39 = Rs. 195.

(2) The highest mark group is 40-49. The number o f students belonging to this group is 17. Hence, the total amount o f money required to distribute the prize money is 10 x 17 = Rs. 170

(3) The lowest mark group is 0-9. The number o f students belonging to this group is 27. Hence, the total number o f problems will be solved by the students of this group is 5 x 27 = 135

(4) The total number o f students is 100 (given in the question.

(a) The number of students obtaining marks ranging from 40 - 49 is 17.

The percentage of students belonging to this group is (17/100) x l 00 = 17 %

Hence, the statement is true.

(b) The number o f students obtaining marks ranging from 10 to 29 is 12 + 20 = 32

Hence, the statement is false.

(5) The number o f students getting less than 20 marks is 27 + 12 = 39

(6) The number o f students getting more than 29 marks is 24 + 17 = 41

(7) The number o f students getting marks between 9 to 40 is 12 + 20 + 24 = 56

(8) The number o f students belonging to the highest mark group 40 - 49 is 17.

(9) The number o f students obtaining more than 19 marks is 20 + 24 + 17 = 61

Q8: Read the following bar graph and answer the following questions:

Yaart

(I) What is the information given by the bar graph?

(ii) State each of the following whether true or false.

(a) The number o f government companies in 1957 is that o f 1982 is 1 :9 .

(b) The number o f government companies has decreased over the year 1957 to 1983.

Ans:

(1) The bar graph represents the number o f government companies in India during some years.

(2) (a) The number of companies in 1957 was 50 and the number o f companies in 1982 was 375. Their ratio in that order is 50: 375 = 2:15

Hence, the statement is false.

(b) The height o f the bar graphs increases over the years 1957 to 1983. Hence, the statement is false.

2:15


(i) What information is given by the bar graph?

(ii) Which state is the largest producer o f rice?

(iii) Which state is the largest producer o f wheat?

(iv) Which state has total production o f rice and wheat at its maximum?

(v) Which state has total production o f wheat and rice at its minimum?

Ans:

(1) The bar graph represents the production of rice and wheat in different states of India.

(2) According to the height of the bars corresponding to rice, W.B. is the largest producer of rice.

(3) According to the height of the bars corresponding to wheat. U.P. is the largest producer o f wheat.

(4) U.P. has the maximum total production of rice and wheat, which is 8 + 16 = 24 units

(5) Maharashtra has the minimum total production of rice and wheat, which are exactly 2 + 4 = 6 units.

Q 10: The following bar graph represents the heights (in cm) o f 50 students o f Class XI o f a particular school. Study the graph and answer the

following questions:

(i) What percentage o f the total number o f students have their heights more than 149 cm?

(ii) How many students in the class are in the range o f maximum height o f the class?

(iii) The school wants to provide a particular type of tonic to each student below the height o f 150 cm to improve his height. If the cost o f the

tonic for each student comes out to be Rs. 55, how much amount o f money is required?

(iv) How many students are in the range o f shortest height o f the class?

(v) State whether true or false:

(a) There are 9 students in the class whose heights are in the range o f 155-159 cm.

(b) Maximum height (in cm ) o f a student in the class is 17.

(c) There are 29 students in the class whose heights are in the range o f 145-154 cm.

(d) Minimum height (in cm ) of a student is the class is in the range of 140-144 cms.

(e) The number o f students in the class having their heights less than 150 cm is 12.

(f) There are 14 students each o f whom has height more than 154. cm.

Ans:

(1) The total number o f students is 50. The number o f students having heights more than 149 cm i.e desired percentage is:

=> =(17 + 9 + 5)/50x100

=> = 62 %

(2) The maximum range of height is 164-165 cm. The number of students belonging to this group is 5.

(3) The number o f students whose heights are less than 150 cm is 7 + 12 = 19. Hence, the total cost is 19 x 55 = Rs.1045/-

(4) The minimum range of height is 140 - 144 cm. The number of students belonging to this group is 7. (5) (a) The number of students whose heights are in the range 155 - 159 cm is 9. Hence, the statement is true.

(b) The maximum possible height (in cm) o f a student in the class can be 164 cm. Hence the statement is false.

(c) The number o f students whose heights are in the range 145-154 cm is 12 +17 = 29. Hence, the statement is true.

(d) The minimum range of heights o f students in the class is 140-144 cm. Hence, the statement is true.

(e) The number o f students having heights less than 150 cm is 7 +12 =19. Hence, the statement is false.

(f) The number of students having heights more than 154 cm is9 + 5 = 14. Hence, the statement is true.

Q 11: Read the following bar graph and answer the following questions:


(ii) What was the production o f cement in the year 1980-81 ?

(iii) What are the minimum and maximum production o f cement and corresponding years?

Ans:

(1) The bar graph represents the industrial production of cement in different years in India.

(2) According to the height of the 6th bar from the left, the production o f cement in the year 1980-81 was 186 lakh tonnes.

(3) According to the heights o f the bars. The minimum production of cement is 30 lakh tonnes in the year 1950 - 51 and the maximum production of cement is 232 lakh tonnes in the year 1982 - 83.

Q12: The bar graph shown in figure represents the circulation of newspapers in 10 languages.

Study the bar graph and answer the following questions:

(i) What is the total number o f newspapers published in Hindi, English, Urdu, Punjabi, and Bengali?

(ii) What percent is the number o f newspapers published in Hindi o f the total number o f newspapers?

(iii) Find the excess o f the number o f newspapers published in English over those published in Urdu.

(iv) Name two pairs o f languages which publish the same number o f newspapers.

(v) State the language in which the sm allest number o f newspapers are published.

(vi) State the language in which the largest number o f newspapers are published.

(vii) State the language in which the number o f newspapers published is between 2500 and 3500.

(viii) State whether true or false:

(a) The number o f newspapers published in Malayalam and Marathi together is less than those published in English.

(b) The number o f newspapers published in Telugu is more than those published in Tam il.

Ans:

(1) The total number o f news papers published in Hindi, English, Urdu, Punjabi and Bengali is = 3700 + 3400 + 700 + 200 + 1100 = 9100.

(2) The total number o f news papers published is = 1100 + 3400 + 1100 + 3700 + 1400 + 1400 +200 + 1000 + 400 + 700 = 14400.

The number of news papers published in Hindi is 3700. The percentage of published Hindi news papers is (3700/ 14400) x 100 = 3700 /1 44 = 25.7%

(3) The number o f news papers published in English and Urdu are 3400 and 700 respectively. Hence, the excess of the number of news papers published in English over those published in Urdu is

= 3400 - 700 = 2700

(4) According to the length of the 5th and 6th bars from the top, the number o f news papers published in Marathi and Malayalam are same. According to the length of the 1 st and 3rd bars from the bottom, the number of news papers published in Bengali and Gujrati are same.

(5) According to the length of the 4th bar from the top, the smallest number of news papers published in the language Punjabi.

(6) According to the length of the 4th bar from the bottom, the largest number of news papers published in the language Hindi.

(7) The languages in which the number of published news papers is greater than or equal to 2500 are English and Hindi. Among the languages Hindi and English, the language in which the number o f published news papers is less than or equal to 3500 is English. Hence, the language is English.

(8)

(a) The number of news papers published in Malayalam and Marathi together is 1400 +1400 = 2800 The number of news papers published in English is 3400. Clearly, 2800 is less than 3400. Hence, the statement is true.

(b) The number o f news papers published in Telugu and Tamil are 400 and 1000 respectively. Clearly 400 is not greater than 1000. Hence, the statement is false.

Q13: Read the bar graph given in and answer the following questions:


(ii) What was the crop-production o f rice in 1970-71 ?

(iii) What is the difference between the maximum and minimum production o f rice?

Ans:

(1) The bar graph represents the production of the rice crop in India in different years.

(2) According to the height of the 3rd bar from the left, the crop-production of rice in 1970-71 is 42.5 lakh tonnes.

(3) The maximum product of rice is 55 lath tonnes (height o f the 4th bar from the left) in the year 1980-81 and the minimum product of rice is 22 lath tonnes (height o f the 1st bar from the left) in the year 1950-51. Hence, the difference between maximum and minimum production of rice (in lath tonnes) is 55 - 22 = 33

Q14:. Read the bar graph given in figure and answer the following questions:

(i) What information does it give?

(ii) In which part the expenditure on education is maximum in 1980?

(iii) In which part the expenditure has gone up from 1980 to 1990?

(iv) In which part the gap between 1980 and 1990 is maximum?

Ans:

(1) The bar graph represents the public expenditure on education in different countries and sub continents in the years 1980 and 1990.

(2) The expenditure on education in Africa in 1980 is the maximum.

(3) It is clear from the bar graph that in East Africa the expenditure has gone up from 1980 to 1990.

(4) It is observed from the bar graph that the gap between expenditures in 1980 and 1990 is maximum in Africa, which is 18 -14 = 4 %

Q15: Read the graph given in figure and answer the following question

(i) What information is given by the bar given?

(ii) In which years the areas under the sugarcane crop were the maximum and the minimum?

(iii) State whether true or false:

The area under sugarcane crop in the year 1982-83 is three tim es that o f the year 1950-51.

Ans:

(1) The bar graph represents the areas (in lath hectares) under sugarcane crop during different years in India.

(2) It is seen from the bar graph that the area under the sugarcane crop is maximum in the year 1982-83 and minimum in the year 1950-51.

(3) The area under the sugarcane crop in the years 1982-83 and 1950-51 are 34 lakh hectares and 18 lakh hectares respectively. Clearly, 34 is not equal to 3 multiplied by 18. Hence, the statement is false.

Q16: Read the bar graph given in figure and answer the following questions:


(ii) What was the expenditure on health and fam ily planning in the year 1982-83?

(iii) In which year is the increase in expenditure maximum over the expenditure in the previous year? W hat is the maximum increase?

Ans:

(1) The bar graph represents the expenditure (in 100 Crores of rupees) on health and family planning during the Sixth Five Year Plan in India.

(2) The height o f the 2nd bar from the left is 7 units, which is corresponding to the year 1982-83. Hence, the expenditure on health and family planning in the year 1982-83 was 700 Crores rupees.

(3) Take the year 1980-81 as the initial year of expenditure. Then:

(a) The increase in expenditure in the year 1981-82 is 5 — 4 = 1 unit

(b) The increase in expenditure in the year 1982-83 is 7 — 5 = 2 units.

(c) The increase in expenditure in the year 1983-84 is 8 — 7 = 1 unit

(d) The increase in expenditure in the year 1984-85 is 10.2 — 8 = 2.2 units.

Hence, in the year 1984-85 the increase in expenditure is the maximum and the maximum increase is 2.2 x 100 = 220 Cores rupees

Q17: Read the bar graph given in figure and answer the following questions:


(ii) What is the number o f fam ilies having 6 members?

(iii) How many members per fam ily are there in the maximum number o f fam ilies? Also tell the number of such fam ilies.

(iv) What are the number of members per fam ily for which the number of fam ilies are equal? Also, tell the number o f such families?

Ans:

(1) The bar graph represents the number o f families with the different number of members in a locality.

(2) The number o f families having 6 members is 50, the height o f the 6th bar from the left.

(3) The maximum number o f families is 120. There are 3 members per family in the maximum number of families.

(4) It is seen from the bar graph that the height o f the 9th and 10th bars from the left are same (equals to 5). Hence, the numbers o f members per family for which the number of families are equal are 9 and 10. The number of such families is 5.

Q18: Read the bar graph given in Fig. and answer the following questions:


(ii) Which Doordarshan center covers maximum area? Also, tell the covered area.

(iii) What is the difference between the areas covered by the centers at Delhi and Bombay?

(iv) Which Doordarshan centers are in U.P. State? What are the areas covered by them?

Ans:

(1) The bar graph represents the area of coverage (in 1000 square km) of some Doordarshan Centers o f India.

(2) It is seen from the bar graph that the height o f the 4th bar from the left is maximum, which is corresponding to Kolkata. Hence, the Kolkata Doordarshan covers a maximum area. The area covered by Kolkata Doordarshan is 36 x 1000 = 36000 sq.km

(3) The area covered by Delhi Doordarshan is 34 x 1000 = 34000 sq.km The area covered by Mumbai Doordarshan is 20 x 1000 = 20000 sq.km Their difference is 34000 — 20000 = 14000 sq. km.

(4) The Doordarshan centers in Kanpur and Lucknow are in the U.P. state. The area covered by Kanpur Doordarshan is 32x1000 = 32000 sq.km The area covered by Lucknow Doordarshan is 25 x 1000 = 25000 sq.km

RD Sharma Solutions Class 9 Graphical Representation Of Statistical Data Exercise23.2

RD Sharma Solutions Class 9 Chapter 23 Exercise 23.2

Q1: Explain the reading and interpretation of bar graphs.

Ans: A bar graph is a diagram consisting of a sequence of vertical or horizontal bars or rectangles, each of which represents an equal interval of the values of a variable, and has the height proportional to the quantities of the phenomenon under consideration in that interval. A bar graph may also be used to illustrate discrete data, in which case each bar represents a distinct circumstance.

While drawing a bar graph, we keep in mind that:

1. The width of the bars should be uniform throughout.

2. The gap between any two bars should be uniform throughout.

3. Bars may be either horizontal or vertical.

Each bar must be of the same width and the gap between them must be uniform. Make sure that the width of the bars and the gap between them should not be necessarily same.


(i)What information is given by the bar graph?

{ii) In which year the export is minimum?

(iii) ln which year the import is maximum?

(iv) In which year the difference of the values of export and import is maximum ?

Y«m

Ans:

(1) The bar graph represents the import and export (in 100 Crores of rupees) from 1982-83 to 1986-87.

(2) The export is minimum in the year 1982-83 at the height of the bar corresponding to export is minimum in the year 1982-83.

(3) The import is maximum in the year 1986-87 as the height of the bar corresponding to import is maximum in the year 1986-87.

(4) The bars of export and import are side by side. Clearly, it is seen from the bar graph that the difference between the values of export and import is maximum in the year 1986-87.

It is seen from the bar graph that the height of the 3s bar from the left is least, which is corresponding to DCE. Hence, the requirement is least in DCE.

Q3: The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph (Fig. 23.28) and choose the correct alternative in each of the following:

(i) The pair of classes in which the results of boys and girls are inversely proportional are:

(a) VI, VIII (b) VI, IX (c) VII, IX (d) VIII, X

(ii) The class having the lowest failure rate of girls is:

(a) VI (b) X (c) IX (d) VIII

(iii) The class having the lowest pass rate of students is:

(a) VI (b) VII (c) VIII (d) IX

Ans:

(1) The pair of classes in which the results of boys and girls are inversely proportional are VI and IX.

(2) The lowest failure rate of girls is same to the highest pass rate. Hence, the class having the lowest failure rate of girls is VII (the height of the bar corresponding to girls for this class is maximum).

(3) The sum of the heights of the bars for boys and girls in class VII is minimum, which is 95 + 40 = 135. Hence, the class having the lowest pass rate is VII. Hence, the correct choice is (b).

Q4: The following data gives the number (in thousands) of applicants registered with an Employment Exchange during 1995-2000:

Year 1995 1996 1997 1998 1999 2000

Number of applicantsregistered(in 18 20 24 28 30 34thousands)

Construct a bar graph to represent the above data.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the number of applicants registered in thousands respectively. We have to draw 6 bars of different lengths given in the table. At first we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the number of applicants registered.

The vertical bar graph of the given data is following:

Q5: The production of saleable steel in some of the steel plants of our country during 1999 is given below:

Plant Bhilai

Production(in thousands 160

Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousand tonnes.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the plants and the production in thousand tonnes respectively. We have to draw 4 bars of different lengths given in the table.

The scale 1 big divisions must be 20 thousand tonnes. So, fast find the heights of the bars corresponding to different plants. After that, we follow the well known procedure.

The heights of the different bars are:

1. The height of the bar corresponding to Bhilai 160/20 = 8 big division.2 The height of the bar corresponding to Durgapur is 80/20 = 4 big divisions.3. The height of the bar corresponding to Rourkela =10 big divisions.4. The height of the bar corresponding to Bokaro is = 7.5 big divisions.

At first we mark 4 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the productions. The vertical bar graph of the given data is following:

Note that one big division in the vertical axis is equivalent to 20 thousand tonnes

Q6: The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:

Year 1960-61 1970-71 1980-81 1990-91 2000-2001

98

Represent the above data with the help of a bar graph.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the route lengths in thousand km respectively. We have to draw 5 bars of different lengths given in the table.

At first we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the route lengths.


Year 1992 1993 1994 1995 1996

Loan(in corers of 2fJ 33 55 55 80rupees)

(i) Represent the above data with the help of a bar graph.

(ii) With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding year.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the amount of loan in Crores of rupees respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the amount of loan disbursed by the bank.

(1) The vertical bar graph of the given data is following:

m i m i i m

Tut

(2) It is seen from the bar graph that the heights of the bars in the years 1994 and 1995 are same. Hence, the amount of loan is not increased in the year 1995 over the preceding year 1994.

Q8: The following table shows the interest paid by a company (in lakhs):

Year 1995-96 1996-97 1997-98 1998-99 1999-2000

lnterest(in lakhs of 2Q 25 15 18 30rupees)

Draw the bar graph to represent the above information.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the interests in lakhs of rupees respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the interests paid by the company.


Q9: The following data shows the average age of men in various countries in a certain year.

Average age(in years)

52 60 50 70 75

Represent the above information by a bar graph.


Let us consider that the horizontal and vertical axes represent the countries and the average age of men's respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the average age of men's in different countries.


■ r

I 1-< jj.

H a torpm O in i ta k ilin U t U lACountry

Q10: The following data gives the production of food grains (In thousand tonnes) for some years:

Production (in thousand rupees)


Ans:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the production of food grains in thousand tonnes respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the production of food grains. The vertical bar graph of the given data is following:

Q11: The following data gives the amount of manure (in thousand tones) manufactured by a company during some years:

Manure(in thousand tones) 35 45 30 40 20

(i) Represent the above data with the help of a bar graph.

(ii) Indicate with the help of the bar graph the year in which the amount of manufactured by the company was maximum.

(iii) Choose the correct alternative:

The consecutive years during which there was the maximum decrease in manure production are:

(a) 1994 and 1995 (b) 1992 and 1993 (c) 1996 and 1997 (d) 1995 and 1996

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the amount of manure in thousand 9 ones respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the amount of manures manufactured by the company.

(1) The vertical bar graph of the given data is following:

(2) It is seen from the bar graph that the height of the 3s bar from the left is maximum, which is corresponding to the year 1994. So in 1994, the quantity manufactured by the company was maximum.

(3) It is seen from the bar graph that the manure production is decreased in the years 1995 (1.5 scale divisions) and 1997 (2 full-scale divisions). So, the maximum decrease is in the year 1997. Hence, the correct choice is (c).

Q12: The following data gives the demand estimates of the Government of India, Department of Electronics for the personnel in the Computer sector during the Eighth Plan period (1990-95):

Qualifications MCA(masters in DCA(diploma in DCE(diploma in CL(certificate levelcomputer applications) computer applications computer engineering) course) ST(short term course)

Personnel required 40600 181600 18600 670600 1802900

Represent the data with the help of a bar graph. Indicate with the help of the bar graph the course where the estimated requirement is least.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the qualifications and the personnel required in hundreds respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the number of personnel required.


It is seen from the bar graph that the height of the 3ffl bar from the left is least, which is corresponding to DCE. Hence, the requirement is least in DCE.

Q13: The income and expenditure for 5 years of a family is given in the following data:

Represent the above data by a bar graph.

Expenditure (Rs. in thousands)

80 130 145 160

1999-2000

210

190

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the income or expenditure in thousand rupees respectively. We have to draw 5 bars for each income and expenditure side by side of different lengths given in the table.

At first, we mark 5 points for each income and expenditure in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the corresponding income or expenditures.

Q14: The investments (in ten crores of rupees) of Life Insurance Corporation of India in different sectors is given below:

Sectors Investment (in ten crores of rupess)

Central government securities 45

State government securities 11

Securities guaranteed by the government 23

Private sectors 18

Socially oriented sectors(plan) 46

Socially oriented sectors(Non - plan) 11


Ans:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the sectors and the investment in ten Crores of rupees respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the investments of Life Insurance Corporation of India. The vertical bar graph of the given data is following:

The short forms used in the graph are:

(a) C.G.S.: Central Government Securities

(b) S.G.S.: State Government Securities

(c) S.G.G.: Securities Guaranteed by Government

(d) RS.: Private Sectors

(e) S.O.S.(P): Socially Oriented Sectors (Plan)

(f) S.O.S.(NP): Socially Oriented Sectors (Non-Plan)

Q15: The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:

Years 1982-83 1983-84 1984-85 19985-86 19986-87

Value of exports ofcotton textiles(in crores 300 325 475 450 550of rupees)

Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the value of Indian export of cotton textiles in Crores of rupees respectively. We have to draw 5 bars of different lengths given in the table.

At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the values of Indian export of cotton textiles in different years. The vertical bar graph of the given data is following:

The export increases in the years 1983-84,1984-85 and 1986-87. Now,

(a) The rate of increase in the year 1983-84 is

325-300 „ 1 n n => - 3 0 0 - X 1 0 0

= > f

= 8.33%

(b) The rate of increase in the year 1984-85 is

475-325 w => 325 X 1 0 0

=> 15000/ 325

=> 600/13

=> 46.15%

(c) The rate of increase in the year 1986-87 is

=> 450 X 1 0 0

=>10000/450

=> 22.22%

Hence, in the year 1984-85, the rate of increase of export is the maximum over the preceding year.

Q16: The following table gives the quantity of goods (in crores of rupees)

Quantity of goods(in crore tonnes)

16 20 20 22 26

Represent this information with the help of a bar graph.

Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the quantity of goods in Crores tonnes respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the quantity of goods carried by Indian railways in different years.


f I “‘ lJ4 »

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It is seen from the bar graph that the quantity of goods carried in the years 1950-51 and 1965-66 are 20 Crores tonnes and 9 Crores tonnes. Clearly 20 is more than 2 multiplied by 9. Hence, the statement is true.

Q17: The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:

Refinery Barauni Koyali Mathura Mumbai Florida

Production of oil(in lakh tonnes) 30 70 40 45 25

Construct a bar graph to represent the above data so that the bars are drawn horizontally.

Ans: To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let u consider that the vertical and horizontal axes represent the refineries and the production of oil in la] tonnes respectively. We have to draw 5 bars of different lengths given in the table.

At first, we mark 5 points in the vertical axis at equal distances and erect rectangles of the same wk at these points. The lengths of the rectangles are proportional to the productions of oil.

The horizontal bar graph of the given data is following:

0 U n W W B O I O ’O M N iK to ifO l

l i t * I w i l l

Q18: The expenditure (in 10 crores of rupees) on health by the Government of India during the various five-year plans is shown below:

Plans 1 II III IV V VI

Expenditure on health(in 10 crores of rupees)

7 14 23 34 76 182

Construct a bar graph to represent the above data.


Let us consider that the horizontal and vertical axes represent the years and the expenditures on health in 10 Crores rupees respectively. We have to draw 6 bars of different lengths given in the table.

At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the expenditures on health by the government of India in different years.


I* Uni

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