RS Aggarwal Class 7 Mathematics Solutions Chapter 22 Bar Graph

Question 1. Describe what a bar graph is and explain its purpose.
Answer: A bar graph consists of rectangular bars with lengths that are proportional to the values they represent. It is used to visually compare data across different categories or time periods. A double bar graph, for example, allows you to compare values for two consecutive years side by side, making it easy to spot patterns and differences at a glance.

Exam Tip: When describing a bar graph, always mention its key feature - that the bar heights are directly proportional to the values - and explain what type of comparison it helps you make.

Question 2. Explain the process for drawing a bar graph step by step.
Answer: To construct a bar graph, follow these five steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the categories (subjects, sports, countries, etc.) at points taken at uniform intervals.
Step 3 - Choose an appropriate scale. For example, you might decide that 1 big division equals 10 marks and 1 small division equals 1 mark, depending on the range of your data.
Step 4 - Calculate the heights of the various bars. Each data value needs to be converted to a height using your chosen scale. For instance, if a value is 43 and your scale is "1 big division = 10 marks, 1 small division = 1 mark," then 43 becomes 4 big divisions and 3 small divisions.
Step 5 - Draw bars of equal width on the x-axis. Make sure the spacing between bars is uniform and matches the spacing between the labels.

Exam Tip: Students often forget to use a consistent scale throughout. Always state your scale clearly and apply it uniformly to all bars so the graph is accurate and easy to read.

Question 3. Draw a bar graph showing the participation of students in different sports given the following data: Cricket = 75 students, Football = 35 students, Tennis = 50 students, Badminton = 25 students, Swimming = 65 students.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the sports at points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 10 students
1 small division = 1 student
Step 4 - Calculate the heights of the various bars:
Cricket = 75 small divisions = 7 big divisions and 5 small divisions
Football = 35 small divisions = 3 big divisions and 5 small divisions
Tennis = 50 small divisions = 5 big divisions
Badminton = 25 small divisions = 2 big divisions and 5 small divisions
Swimming = 65 small divisions = 6 big divisions and 5 small divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: Always verify that your scale choice allows all data values to fit on the graph without exceeding the paper boundaries, and double-check your division calculations.

Question 4. Draw a bar graph showing scooter sales data from 2004 to 2009 with the following values: 2004 = 550, 2005 = 700, 2006 = 900, 2007 = 1100, 2008 = 1400, 2009 = 1600.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the years at points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 2000 scooters
1 small division = 200 scooters
Step 4 - Calculate the heights of the various bars:
2004 = 55 small divisions = 5 big divisions and 5 small divisions
2005 = 70 small divisions = 7 big divisions
2006 = 62.5 small divisions = 6 big divisions and 2.5 small divisions
2007 = 87.5 small divisions = 8 big divisions and 7.5 small divisions
2008 = 75 small divisions = 7 big divisions and 5 small divisions
2009 = 120 small divisions = 12 big divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: When dealing with larger numbers, select a scale with bigger divisions to avoid using excessive space. Check that your calculated bar heights fit comfortably within your graph paper.

Question 5. Draw a bar graph showing the exports (in units) for five countries with the following data: China = 84 units, India = 70 units, Germany = 28 units, U.K. = 56 units, Sweden = 42 units.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the countries at points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 5 units
2 small divisions = 1 unit
Step 4 - Calculate the heights of the various bars:
China = 84 small divisions = 8 big divisions and 4 small divisions
India = 70 small divisions = 7 big divisions
Germany = 28 small divisions = 2 big divisions and 8 small divisions
U.K. = 56 small divisions = 5 big divisions and 6 small divisions
Sweden = 42 small divisions = 4 big divisions and 2 small divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: Ensure your scale is chosen such that even the smallest data value is clearly visible on the graph with a noticeable bar height.

Question 6. Draw a bar graph representing the population in millions for the following years: 2001-2002 = 36 million, 1961 = 43.2 million, 1971 = 54 million, 1981 = 68.4 million, 1991 = 85.2 million, 2001 = 102 million.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the year at the points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 100 million
1 small division = 10 million
Step 4 - Calculate the heights of the various bars:
1951 = 36 small divisions = 3 big divisions and 6 small divisions
1961 = 43.2 small divisions = 4 big divisions and 3.2 small divisions
1971 = 54 small divisions = 5 big divisions and 4 small divisions
1981 = 68.4 small divisions = 6 big divisions and 8.4 small divisions
1991 = 85.2 small divisions = 8 big divisions and 5.2 small divisions
2001 = 102 small divisions = 10 big divisions and 2 small divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: For population data spanning decades, choose a larger scale unit so that all years can be displayed together without the graph becoming too cluttered.

Question 7. Draw a bar graph showing the population distribution of states in India with the following data: Bihar = 82 lakhs, Jharkhand = 27 lakhs, Uttar Pradesh = 106 lakhs, Uttarakhand = 8 lakhs, Madhya Pradesh = 60 lakhs, Chhattisgarh = 21 lakhs.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the states at the points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 100 lakhs
1 small division = 10 lakhs
Step 4 - Calculate the heights of the various bars:
Bihar = 82 small divisions = 8 big divisions and 2 small divisions
Jharkhand = 27 small divisions = 2 big divisions and 7 small divisions
Uttar Pradesh = 106 small divisions = 10 big divisions and 6 small divisions
Uttarakhand = 8 small divisions
Madhya Pradesh = 60 small divisions = 6 big divisions
Chhattisgarh = 21 small divisions = 2 big divisions and 1 small division
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: When comparing regions with very different population sizes (like Uttarakhand with 8 lakhs versus Uttar Pradesh with 106 lakhs), your chosen scale must accommodate the largest value while still showing smaller values distinctly.

Question 8. Draw a bar graph displaying the population growth in crores of rupees across multiple years: 1998-99 = 70 crores, 1999-2000 = 84 crores, 2000-2001 = 98 crores, 2001-2002 = 106 crores, 2002-2003 = 120 crores.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the years at the points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 10 thousand crore rupees
1 small division = 1 thousand crore rupees
Step 4 - Calculate the heights of the various bars:
1998-99 = 70 small divisions = 7 big divisions
1999-2000 = 84 small divisions = 8 big divisions and 4 small divisions
2000-2001 = 98 small divisions = 9 big divisions and 8 small divisions
2001-2002 = 106 small divisions = 10 big divisions and 6 small divisions
2002-2003 = 120 small divisions = 12 big divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: For financial data showing growth trends, a bar graph clearly reveals increases or decreases year by year, making it ideal for analyzing economic patterns.

Question 9. Draw a bar graph representing the distance from home to various cities: Kolkata = 134 km, Mumbai = 110 km, Chennai = 170 km, Hyderabad = 122 km.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the cities at the points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 100 km
1 small division = 10 km
Step 4 - Calculate the heights of the various bars:
Kolkata = 134 small divisions = 13 big divisions and 4 small divisions
Mumbai = 110 small divisions = 11 big divisions
Chennai = 170 small divisions = 17 big divisions
Hyderabad = 122 small divisions = 12 big divisions and 2 small divisions
Step 5 - Draw bars of equal width on the x-axis. The spacing between the two bars should also be the same.

Exam Tip: For distance data, ensure your scale unit (here, 100 km) is appropriate to the data range so that the graph remains readable and proportional.

Question 10. Draw a bar graph showing the import values (in thousand crore rupees) for the fiscal years 2001-02 to 2005-06 with the following data: 2001-02 = 148, 2002-03 = 178, 2003-04 = 204, 2004-05 = 232, 2005-06 = 180.
Answer: We can construct the bar graph by following the given steps:
Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.
Step 2 - Along OX, write the names of the months at the points taken at uniform intervals.
Step 3 - Choose the scale:
1 big division = 5 cm
2 small divisions = 1 cm
Step 4 - Calculate the heights of the various bars:
June = 50 small divisions = 5 big divisions
July = 60 small divisions = 6 big divisions
August = 80 small divisions = 8 big divisions
September = 40 small divisions = 4 big divisions
October = 20 small divisions = 2 big divisions
November = 10 small divisions = 1 big division

Exam Tip: When working with import or export data, ensure that your scale allows the largest value to fit on the page while maintaining clarity for smaller values.

Question 14. Draw a bar graph for the data given below:
The number of students using different brands of shoes:
Brand A - 45, Brand B - 25, Brand C - 15, Brand D - 10, Brand E - 5
Answer: To create a bar graph, follow these steps:

Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.

Step 2 - Along OX, mark the names of the brands at uniform gaps.

Step 3 - Pick an appropriate scale:
1 big division = Rs. 500
1 small division = Rs. 50

Step 4 - Calculate the heights of the bars:
Brand A = 45 small divisions = 4 big divisions and 5 small divisions
Brand B = 25 small divisions = 2 big divisions and 5 small divisions
Brand C = 15 small divisions = 1 big division and 5 small divisions
Brand D = 10 small divisions = 1 big division
Brand E = 5 small divisions

Step 5 - Draw bars of equal width on the x-axis. The spacing between two bars should remain consistent.

The resulting bar graph displays the brands on the horizontal axis and the number of students on the vertical axis, with each brand represented by a rectangular bar whose height corresponds to the number of students wearing that brand.

Exam Tip: Always choose a scale that fits your graph paper and ensures all bars are clearly visible. Make sure the spacing between bars is uniform and consistent.

Question 15. Draw a bar graph showing the sales data for four weeks:
Week 1 - 8500, Week 2 - 9000, Week 3 - 9500, Week 4 - 9000
Answer: To construct a bar graph, follow these steps:

Step 1 - On graph paper, draw a horizontal line OX as the x-axis and a vertical line OY as the y-axis.

Step 2 - Along OX, mark the week names at uniform intervals.

Step 3 - Choose an appropriate scale:
1 big division = 50 students
1 small division = 5 students

Step 4 - Determine the heights of the various bars:
School bus = 128 small divisions = 12 big divisions and 8 small divisions
Private bus = 72 small divisions = 7 big divisions and 2 small divisions
Bicycle = 98 small divisions = 9 big divisions and 8 small divisions
Rickshaw = 42 small divisions = 4 big divisions and 2 small divisions
By foot = 30 small divisions = 3 big divisions

Step 5 - Draw bars of uniform width along the x-axis. The spacing between the two bars should also be consistent.

The final bar graph shows the modes of transport on the horizontal axis and the number of students on the vertical axis, with each bar's height representing the corresponding number of students.

Exam Tip: Verify your scale selection ensures all data points fit comfortably on the graph without crowding or excessive blank space.

Question 16. Interpret the bar graph and answer the following:
(i) What does the bar graph show?
(ii) In which subject is the student very good?
(iii) In which subject is the student poor?
(iv) Calculate the average marks.
Answer:
(i) The bar graph displays the marks earned by a student across multiple subjects in an examination.

(ii) The student performs very well in mathematics.

(iii) The student is not strong in Hindi.

(iv) The marks obtained across subjects are:
Marks in English = 60
Marks in Hindi = 35
Marks in Mathematics = 75
Marks in Social Science = 50
Marks in Science = 60

Average marks = \( \frac{60 + 35 + 75 + 50 + 60}{5} = \frac{280}{5} = 56 \)

Exam Tip: When interpreting bar graphs, always read values carefully from the y-axis and double-check your arithmetic when computing sums and averages.

Question 17. Examine the bar graph showing family sizes and answer:
(i) What data does the bar graph present?
(ii) How many families have exactly three members?
(iii) How many individuals are living as sole occupants?
(iv) Which family size is most frequent?
Answer:
(i) The bar graph illustrates the number of members within each of 85 families.

(ii) Forty families consist of three members each.

(iii) Number of people living alone = 85 - (5 + 40 + 25 + 15)
= 85 - 85
= 0

(iv) The most typical family composition includes three members. Every such family has exactly three members.

Exam Tip: When working with grouped data, always ensure your sub-groups add up to the stated total to catch calculation errors early.

Question 18. Analyze the bar graph of mountain heights and provide answers to:
(i) Which peak is the highest and what is its height?
(ii) Find the ratio of the highest peak to the second-highest peak.
(iii) List all peak heights in descending order.
Answer:
(i) Mount Everest ranks as the tallest peak with a height of 8800 m.

(ii) Heights of the peaks:
Highest peak, Mount Everest = 8800 m
Second-highest peak, Kanchenjunga = 8200 m

Ratio = \( \frac{8800}{8200} = \frac{44}{41} = 44 : 41 \)

(iii) The heights of the peaks are 6000 m, 8000 m, 7500 m, 8200 m, and 8800 m.

Heights arranged in descending order:
8800 m, 8000 m, 7500 m, 6000 m

Exam Tip: When simplifying ratios, find the greatest common divisor of both numbers to reduce the ratio to its simplest form.