Data Handling – III (Bar Graphs Exercise 23.2) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

 Page 1


 
 
 
 
 
  
                                                                           
1. Explain the reading and interpretation of bar graphs. 
Solution: 
 
A graph with its length proportional to the value it represents is called a bar graph. The bars can either be plotted 
horizontally or vertically. It is basically a visual display which is used to compare the amount of occurrence of 
various characteristics of data. 
Bar graph help us to 
(i) Compare the groups of data 
(ii) Generalize the data 
 
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: 
 
Consider a chart by using data from the bar graph: 
Page 2


 
 
 
 
 
  
                                                                           
1. Explain the reading and interpretation of bar graphs. 
Solution: 
 
A graph with its length proportional to the value it represents is called a bar graph. The bars can either be plotted 
horizontally or vertically. It is basically a visual display which is used to compare the amount of occurrence of 
various characteristics of data. 
Bar graph help us to 
(i) Compare the groups of data 
(ii) Generalize the data 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
 
 
 
  
 
(i) The bar graph gives us information regarding import and export from 1982-83 to 1886-87. 
 
(ii) The export is minimum in the year 1982-83. 
 
(iii) The import is maximum in the year 1986-87. 
 
(iv) The difference of the values of import and export is maximum in the year 1986-87. 
 
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 
Page 3


 
 
 
 
 
  
                                                                           
1. Explain the reading and interpretation of bar graphs. 
Solution: 
 
A graph with its length proportional to the value it represents is called a bar graph. The bars can either be plotted 
horizontally or vertically. It is basically a visual display which is used to compare the amount of occurrence of 
various characteristics of data. 
Bar graph help us to 
(i) Compare the groups of data 
(ii) Generalize the data 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
 
 
 
  
 
(i) The bar graph gives us information regarding import and export from 1982-83 to 1886-87. 
 
(ii) The export is minimum in the year 1982-83. 
 
(iii) The import is maximum in the year 1986-87. 
 
(iv) The difference of the values of import and export is maximum in the year 1986-87. 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
(i) The option (b) is the correct answer.  
The pair of classes in which the results of boys and girls are inversely proportional are VI, IX. 
We know that 
In class VI  
% of boys = 80 
% of girls = 70 
In class IX  
% of boys = 70 
% of girls = 80 
 
(ii) The option (a) is the correct answer.  
The class having the lowest failure rate of girls is VII. 
We know that the passing percentage of girls in Class VII is 100%. 
So 0% of girls have failed in this class. 
 
(iii) The option (b) and (c) are the correct answers.  
The class having the lowest pass rate of student is VII and VIII. 
We know that the sum of vertical heights of % of boys and girls in class VII and VIII is same i.e. 140 units and 
the sum is least compared to other classes. 
 
4. The following bar graph shows the number of persons killed in industrial accidents in a country for some 
years (Fig.23.23). 
Page 4


 
 
 
 
 
  
                                                                           
1. Explain the reading and interpretation of bar graphs. 
Solution: 
 
A graph with its length proportional to the value it represents is called a bar graph. The bars can either be plotted 
horizontally or vertically. It is basically a visual display which is used to compare the amount of occurrence of 
various characteristics of data. 
Bar graph help us to 
(i) Compare the groups of data 
(ii) Generalize the data 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
 
 
 
  
 
(i) The bar graph gives us information regarding import and export from 1982-83 to 1886-87. 
 
(ii) The export is minimum in the year 1982-83. 
 
(iii) The import is maximum in the year 1986-87. 
 
(iv) The difference of the values of import and export is maximum in the year 1986-87. 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
(i) The option (b) is the correct answer.  
The pair of classes in which the results of boys and girls are inversely proportional are VI, IX. 
We know that 
In class VI  
% of boys = 80 
% of girls = 70 
In class IX  
% of boys = 70 
% of girls = 80 
 
(ii) The option (a) is the correct answer.  
The class having the lowest failure rate of girls is VII. 
We know that the passing percentage of girls in Class VII is 100%. 
So 0% of girls have failed in this class. 
 
(iii) The option (b) and (c) are the correct answers.  
The class having the lowest pass rate of student is VII and VIII. 
We know that the sum of vertical heights of % of boys and girls in class VII and VIII is same i.e. 140 units and 
the sum is least compared to other classes. 
 
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: 
 
Consider a chart by using data from the bar graph: 
Page 5


 
 
 
 
 
  
                                                                           
1. Explain the reading and interpretation of bar graphs. 
Solution: 
 
A graph with its length proportional to the value it represents is called a bar graph. The bars can either be plotted 
horizontally or vertically. It is basically a visual display which is used to compare the amount of occurrence of 
various characteristics of data. 
Bar graph help us to 
(i) Compare the groups of data 
(ii) Generalize the data 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
 
 
 
  
 
(i) The bar graph gives us information regarding import and export from 1982-83 to 1886-87. 
 
(ii) The export is minimum in the year 1982-83. 
 
(iii) The import is maximum in the year 1986-87. 
 
(iv) The difference of the values of import and export is maximum in the year 1986-87. 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
(i) The option (b) is the correct answer.  
The pair of classes in which the results of boys and girls are inversely proportional are VI, IX. 
We know that 
In class VI  
% of boys = 80 
% of girls = 70 
In class IX  
% of boys = 70 
% of girls = 80 
 
(ii) The option (a) is the correct answer.  
The class having the lowest failure rate of girls is VII. 
We know that the passing percentage of girls in Class VII is 100%. 
So 0% of girls have failed in this class. 
 
(iii) The option (b) and (c) are the correct answers.  
The class having the lowest pass rate of student is VII and VIII. 
We know that the sum of vertical heights of % of boys and girls in class VII and VIII is same i.e. 140 units and 
the sum is least compared to other classes. 
 
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: 
 
Consider a chart by using data from the bar graph: 
 
 
 
 
 
  
 
 
(i) The options (b) and (d) are the correct answer.  
The year which shows the maximum percentage increase in the number of persons killed in coal mines over the 
preceding year is 1997 and 2000. 
 
In the year 1997 the death increased to 300 from 200 and in the year 2000 increased to 200 from 100. 
% increase in death in 1997 = 100% 
% increase in death in 2000 = 100% 
 
(ii) The option (a) is the correct answer. 
The year which shows the maximum decrease in the number of persons killed in industrial accidents over the 
preceding year is 1996. 
 
The year 1996 and 1999 shows the decrease in the amount of persons killed by industrial accidents. 
% decrease in the death in 1996 = 43.75% 
% decrease in the death in 1999 = 30.77% 
 
(iii) The option (a) is the correct answer. 
The year in which the maximum number of persons were killed in industrial accidents other than those killed in 
coal mines is 1995. 
 
1600 persons were killed in the year 1995 due to industrial accidents which is higher when compared to other 
years. 
 
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: 
 
Construct two mutually perpendicular lines OX and OY. 
Let us mark plants along the horizontal line OX and mark production along the vertical line OY. 
Take equal width for each bar on the axis OX. 
Now let us take a suitable scale to find the heights of the bar. 
Take 1 division = 20 thousand tonnes