Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions -Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

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.

 

Q2: 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 ?

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

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:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

(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:

Year199519961997199819992000
Number of applicants registered(in thousands)182024283034

 Construct a bar graph to represent the above data.

 Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

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:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

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

PlantBhilaiDurgapurRourkelaBokaro
Production(in thousands16080200150

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:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

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:

Year1960-611970-711980-811990-912000-2001
Route length(in thousand km)5660617498

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.

The vertical bar graph of the given data is following:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q7: The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:

Year19921993199419951996
Loan(in corers of rupees)2833555580

(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:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

(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):

Year1995-961996-971997-981998-991999-2000
Interest(in lakhs of rupees)2025151830

 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.

The vertical bar graph of the given data is following:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

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

CountryIndiaNepalChinaPakistanU.KU.S.A
Average age(in years)555260507075

Represent the above information by 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 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.

The vertical bar graph of the given data is following:

Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

The document Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on Ex-23.2 (Part - 1), Graphical Representation Of Statistical Data, Class 9, Math RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. What is the importance of graphical representation of statistical data?
Ans. Graphical representation of statistical data is important because it helps in visualizing and understanding the data more easily. It allows us to identify trends, patterns, and outliers in the data, making it easier to make comparisons and draw conclusions. Graphs also make it easier to communicate the data to others, as they provide a clear and concise representation of the information.
2. What are the different types of graphs that can be used to represent statistical data?
Ans. There are several types of graphs that can be used to represent statistical data, including: - Bar graphs: These graphs use rectangular bars to represent the data, with the height of each bar corresponding to the frequency or value of the data. - Line graphs: These graphs use lines to connect data points, showing the trend or change in the data over time. - Pie charts: These graphs use circles divided into sectors to represent the proportion or percentage of different categories within the data. - Histograms: These graphs are similar to bar graphs, but they are used to represent continuous data by dividing it into intervals or bins. - Scatter plots: These graphs use dots or markers to represent individual data points and show the relationship or correlation between two variables.
3. How can we interpret a bar graph?
Ans. To interpret a bar graph, we need to look at the height or length of each bar and understand what it represents. The height of each bar corresponds to the frequency or value of the data it represents. We can compare the heights of different bars to identify which category or data point has the highest or lowest value. Bar graphs also allow us to make comparisons between different categories or groups by visually comparing the heights of the bars.
4. What information can be obtained from a line graph?
Ans. A line graph provides information about the trend or change in the data over time. By plotting data points and connecting them with lines, we can see how the values of the data fluctuate or increase/decrease over a specific period. Line graphs help us identify patterns, trends, and fluctuations in the data, allowing us to make predictions or draw conclusions about the data's behavior.
5. How can we analyze a pie chart effectively?
Ans. To analyze a pie chart effectively, we need to look at the different sectors or slices and understand what they represent. Each sector represents a category or group, and the size of the sector corresponds to the proportion or percentage of that category within the data. We can visually compare the sizes of different sectors to identify which category has the largest or smallest percentage. Pie charts are particularly useful for showing the composition or distribution of data, allowing us to see the relative importance of each category.
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