Graphical Representation of Statistical Data- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


      
Q u e s t i o n : 1 9
Explain the reading and interpretation of bar graphs.
S o l u t i o n :
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 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 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.
Q u e s t i o n : 2 0
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?
Page 2


      
Q u e s t i o n : 1 9
Explain the reading and interpretation of bar graphs.
S o l u t i o n :
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 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 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.
Q u e s t i o n : 2 0
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?
S o l u t i o n :
(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 as 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.
 
Q u e s t i o n : 2 1
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 result of boys and girls are inversely proportional are:
(a) VI, VIII
(b) VI, IX
Page 3


      
Q u e s t i o n : 1 9
Explain the reading and interpretation of bar graphs.
S o l u t i o n :
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 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 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.
Q u e s t i o n : 2 0
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?
S o l u t i o n :
(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 as 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.
 
Q u e s t i o n : 2 1
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 result 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 students is
(a) VI
(b) VII
(c) VIII
(d) IX
S o l u t i o n :
(1) The pair of classes in which the results of boys and girls are inversely proportional are VI and IX. So, (b) is the
correct option.
(2) 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). So, the correct option is (a)
(3) The sum of the heights of the bars for boys and girls in the 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). 
Q u e s t i o n : 2 2
The following data gives the number (in thousands) of applicants registered with an
 
Year 1995 1996 1997 1998 1999 2000
Number of applicants
registered (in thousands)
18 20 24 28 30 34
Construct a bar graph to represent the above data.
S o l u t i o n :
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.
Page 4


      
Q u e s t i o n : 1 9
Explain the reading and interpretation of bar graphs.
S o l u t i o n :
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 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 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.
Q u e s t i o n : 2 0
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?
S o l u t i o n :
(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 as 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.
 
Q u e s t i o n : 2 1
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 result 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 students is
(a) VI
(b) VII
(c) VIII
(d) IX
S o l u t i o n :
(1) The pair of classes in which the results of boys and girls are inversely proportional are VI and IX. So, (b) is the
correct option.
(2) 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). So, the correct option is (a)
(3) The sum of the heights of the bars for boys and girls in the 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). 
Q u e s t i o n : 2 2
The following data gives the number (in thousands) of applicants registered with an
 
Year 1995 1996 1997 1998 1999 2000
Number of applicants
registered (in thousands)
18 20 24 28 30 34
Construct a bar graph to represent the above data.
S o l u t i o n :
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:
Q u e s t i o n : 2 3
The production of saleable steel in some of the steel plants our country during 1999 is given below:
Plant Bhilai Durgapur Rourkela Bokaro
Production
(In thousand tonnes)
160 80 200 150
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20
thousand tonnes.
S o l u t i o n :
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, first 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 is big division.
2. The height of the bar corresponding to Durgapur is big divisions.
3. The height of the bar corresponding to Rourkela is big divisions.
4. The height of the bar corresponding to Bokaro is 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:
Page 5


      
Q u e s t i o n : 1 9
Explain the reading and interpretation of bar graphs.
S o l u t i o n :
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 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 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.
Q u e s t i o n : 2 0
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?
S o l u t i o n :
(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 as 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.
 
Q u e s t i o n : 2 1
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 result 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 students is
(a) VI
(b) VII
(c) VIII
(d) IX
S o l u t i o n :
(1) The pair of classes in which the results of boys and girls are inversely proportional are VI and IX. So, (b) is the
correct option.
(2) 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). So, the correct option is (a)
(3) The sum of the heights of the bars for boys and girls in the 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). 
Q u e s t i o n : 2 2
The following data gives the number (in thousands) of applicants registered with an
 
Year 1995 1996 1997 1998 1999 2000
Number of applicants
registered (in thousands)
18 20 24 28 30 34
Construct a bar graph to represent the above data.
S o l u t i o n :
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:
Q u e s t i o n : 2 3
The production of saleable steel in some of the steel plants our country during 1999 is given below:
Plant Bhilai Durgapur Rourkela Bokaro
Production
(In thousand tonnes)
160 80 200 150
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20
thousand tonnes.
S o l u t i o n :
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, first 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 is big division.
2. The height of the bar corresponding to Durgapur is big divisions.
3. The height of the bar corresponding to Rourkela is big divisions.
4. The height of the bar corresponding to Bokaro is 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 the one big division in the vertical axis is equivalent to 20 thousand tonnes.
Q u e s t i o n : 2 4
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
Route length
(in thousand
km)
56 60 61 74 98
Represent the above data with the help of a bar graph.
S o l u t i o n :
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.
The vertical bar graph of the given data is following:
Q u e s t i o n : 2 5
The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
 
Year 1992 1993 1994 1995 1996
Loan
(in crores of rupees)
 
28 33 55 55 80