Exercise 23.1
Question 1: The following table shows the daily production of T.V. sets in an industry for 7 days of a week:
Solution 1:
Let one TV icon shows 50 TV’s
Question 2: The following table shows the number of Maruti cars sold by five dealers in a particular month:
Represent the above information by a pictograph.
Solution 2:
Let one car icon Shows 5 Maruti cars.
Question 3: The population of Delhi State in different census years is as given below:
Represent the above information with the help of a bar graph.
Solution 3:
Horizontal line (-axis) represents the census year and the vertical line (-axis) represents the population in lakhs.
Question 4: Read the bar graph show in Fig. 23.8 and answer the following questions:
(i) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent?
(iii) Of which state, were the maximum number of tickets sold?
(iv) State whether true or false.
The maximum number of tickets sold is three times the minimum number of tickets sold.
(v) Of which state were the minimum number of tickets sold?
Solution 4:
(i) Above bar graph shows the number of tickets of distinct state lotteries sold by an agent on a day.
(ii) Assam state sold 40 tickets.
(iii) Haryana sold maximum number of tickets.
(iv) False
Maximum Number of Ticket Sold in Haryana = 100 units
Minimum Number of Ticket Sold in Rajasthan = 20 units
The minimum number of tickets is 5 times maximum number of ticket sold.
Hence, the given statement is not true.
(v) Rajasthan state was sold minimum number of tickets.
Question 5: Study the bar graph representing the number of persons in various age groups in a town shown in Fig. 23.9. Observe the bar graph and answer the following questions:
i) It is decided to distribute work books on Mathematics to the students obtaining less than 20 marks, giving one workbook to each of such students. If a work book costs Rs. 5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of Rs. 10. How much amount of 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 of 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 19.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii) What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?
Solution 7:
Bar graph shows the data of 100 students and their marks.
(i) Number of students obtain less than 20 marks = 27 + 12 = 39
Amount per workbook = 5
Amount of the workbooks = 5 × 39
Amount of the workbooks = Rs. 195
(ii) Highest Marks obtain by group 40 – 49 and their number of students is = 17
Total Prize Money required = 10 × 17
Total Prize Money required = Rs. 170
(iii) Lowest marks obtain by group 0 – 9 and their number of students is = 27
Number of problems solved by students = 5 × 27 = 135
(iv) (a) True
(b) False
(v) Number of students with 0 – 9 marks = 27
Number of students with 10 – 19 marks = 12
Total Number of students scoring less than 20 marks = 27 + 12
Total Number of students scoring less than 20 marks = 39
(vi) Number of students with 30-39 marks group = 24
Number of students with 30-39 marks group = 17
Total Number of students scoring more than 29 marks = 24 + 17
Total Number of students scoring more than 29 marks = 41
(vii) Number of students with 10-19 marks group = 12
Number of students with 20-29 marks group = 20
Number of students with 30-39 marks group = 24
Total Number of students scoring 9 to 40 marks = 12 + 20 + 24
Total Number of students scoring 9 to 40 marks = 56
(viii) 17 students obtaining 40-49 marks which is highest marks group.
(ix) Number of students with 20-29 marks group = 20
Number of students with 30-39 marks group = 24
Number of students with 40-49 marks group = 17
Total Number of students scoring 19 marks = 20 + 24 + 17
Total Number of students scoring 19 marks = 61
Question 8: Read the following bar graph (Fig. 23.12) and answer the following questions:
(i) What information is given by the bar graph?
(ii) Which state is the largest producer of rice?
(iii) Which state is the largest producer of wheat?
(iv) Which state has total production of rice and wheat as its maximum?
(v) Which state has the total production of wheat and rice minimum?
Solution 9:
Below schedule is related to given bar graph:
(i) Bar graph shows the information about rice and wheat production in various states of the India.
(ii) West Bengal is the largest producer of rice.
(iii) Uttar Pradesh is the largest producer of wheat.
(iv) Total production of rice and wheat as its maximum in Uttar Pradesh.
(v) Total production of rice and wheat as its minimum in Maharashtra.
Question 10: The following bar graph (Fig. 23.14) represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:
(i) What percentage of the total number of student have their heights more than 149 cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height of 150 cm to improve his height. If the cost of the tonic for each student comes out to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
(a) There are 9 students in the class whose heights are in the range of 155−159 cm.
(b) Maximum height (in cm) of a student in the class is 17.
(c) There are 29 students in the class whose heights are in the range of 145−154 cm.
(d) Minimum height (in cm) of a student is the class is in the range of 140−144 cm.
(e) There are 14 students each of whom has height more than 150 cm.
(f) There are 14 students each of whom has height more than 154 cm.
Solution 10:
Below is the schedule of above bar graph:-
(i) What information is given by the bar graph?
(ii) What was the production of cement in the year 1980-81?
(iii) What is the minimum and maximum productions of cement and corresponding years?
Solution 11:
(i) Above bar graph shows information about industrial production of cement in different years.
(ii) 186 lakh tonnes production of cement in the year 1980-81.
(iii) The minimum production in 1950 – 1951.
The minimum production in 1950 – 1951 is 30 units.
The maximum production in 1982 - 1983.
The maximum production in 1982 – 1982 is 232 units.
Question 12: The bar graph shown in Fig. 23.16 represents the circulation of newspapers in 10 languages. Study the bar graph and answer the following questions:
(i) What is the total number of newspapers published in Hindi, English, Urdu, Punjabi and Bengali?
(ii) What per-cent is the number of newspapers published in Hindi of the total number of newspapers?
(iii) Find the excess of the number of newspapers, published in English over those published in Urdu.
(iv) Name two pairs of languages which publish the same number of newspapers.
(v) State the language in which the smallest numbers of newspapers are published.
(vi) State the language in which the maximum numbers of newspapers is published.
(vii) State the language in which the number of newspapers published is between 2500 and 3500.
(viii) State whether true or false:
(a) The number of newspapers published in Malayalam and Marathi together is less than those published in English.
(b) The number of newspapers published in Telugu is more than those published in Tamil.
Solution 12:
Exercise 23.2
Question 1: Explain the reading and interpretation of bar graphs.
Solution 1: Bar graph is a pictorial representation of a numerical data by a number of bars (rectangle) of equal width erected horizontally or vertically with equal spacing between them.
Use of Bar graph:-
(i) Compare the groups of data
(ii) Generalize the data
Question 2: Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which year the export is minimum?
(iii) In which year the import is maximum?
(iv) In which year the difference of the values of export and import is maximum?
Solution 2:
Below is the data of above bar graph:
(i) The bar graph show us import and export from 1982-83 to 1886-87.
(ii) In year 1982-83 is the minimum export.
(iii) In year 1986-87 is the maximum import.
(iv) In 1986-87 the values of import and export is maximum.
Question 3: The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph (Fig.23.22) and choose the correct option 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) VIII, IX
(d) VIII, X
(ii) The class having the lowest failure rate of girls is:
(a) VII
(b) X
(c) IX
(d) VIII
(iii) The class having the lowest pass rate of student is:
(a) VI
(b) VII
(c) VIII
(d) IX
Solution 3: Below is the data of above the bar graph:
Solution (i) (b)
Boys percentage in class VI = 80
Girls percentage in class VI = 70
Boys percentage in class IX = 70
Girls percentage in class IX = 80
Hence, in class VI and IX are inversely proportional.
Solution (ii) (a)
100% are girls are passed in class VII.
We know that the passing percentage of girls in Class VII is 100%.
Hence, Girls have failed in class VII 0%.
Solution (iii) (b) and (c)
In class VII and VIII the percentage of passing is 140 units.
Question 4: The following bar graph shows the number of persons killed in industrial accidents in a country for some years (Fig.23.23).
Read the bar graph and choose the correct alternative in each of the following:
(i) The year which shows the maximum percentage increase in the number of persons killed in coal mines over the preceding year is:
(a) 1996
(b) 1997
(c) 1999
(d) 2000
(ii) The year which shows the maximum decrease in the number of persons killed in industrial accidents over the preceding year is:
(a) 1996
(b) 1997
(c) 1998
(d) 1999
(iii) The year in which the maximum number of persons were killed in industrial accidents other than those killed in coal mines is:
(a) 1995
(b) 1997
(c) 1998
(d) 1999
Solution 4:
Below is the data of above the bar graph:
(i) (b) and (d)
Increase percentage in death in 1997 = 100%
Increase percentage in death in 2000 = 100%
(ii) (a)
Decrease percentage in the death in 1996 = 43.75%
Decrease percentage in the death in 1999 = 30.77%
(iii) (a)
The year in which the maximum numbers of persons were killed in industrial accidents other than those killed in coal mines is 1995.
Question 5: The production of saleable steel in some of the steel plants of our country during 1999 is given below:
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousand tonnes.
Solution 5:
It is given that the scale use 1 division = 20 thousand tonnes
Heights of the rectangular bars:
Question 6: The following data gives the number (in thousands) of applicants registered with an Employment Exchange during 1995-2000:
Construct a bar graph to represent the above data.
Solution 6:
1 division = 4 thousand applicants
Question 7: The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
Represent the above data with the help of a bar graph.
Solution 7:
Scale = 1 big division = 10 thousand kilometres
Question 8: The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
(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.
Solution 8:
Scale = 1 big division = 10 crores of loan
(ii) The year in which amount of loan is not increased over that of the preceding year is 1995.
Question 9: The following table shows the interest paid by a company (in lakhs):
Draw the bar graph to represent the above information.
Solution 9:
Scale = 1 big division = 5 lakhs of rupees paid as interest by the company
Question 10: The following data shows the average age of men in various countries in a certain year:
Represent the above information by a bar graph.
Solution 10:
Scale = 1 big division = 10 years
Question 11: The following data gives the production of foodgrains (in thousand tonnes) for some years:
Represent the above data with the help of a bar graph.
Solution 11:
Scale = 1 big division = 20 thousand tonnes
Question 12: The following data gives the amount of manure (in thousand tonnes) manufactured by a company during some years:
(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 manure manufactured by the company was maximum.
(iii) Choose the correct alternative:
The consecutive years during which there was maximum decrease in manure production are:
(a) 1994 and 1995
(b) 1992 and 1993
(c) 1996 and 1997
(d) 1995 and 1996
Solution 12:
Scale = 1 big division = 5 thousand tonnes of manure
(ii) In 1994 the maximum amount of manure was manufactured by the company.
(iii) (c)
In 1996 and 1997 the consecutive years during which there was maximum decrease in manure production.