GSEB Class 6 Maths Solutions Chapter 9 Data Handling Exercise 9.4

Question 1. A survey of 120 school students was done to find which activity they prefer to do in their free time.

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most of the students other than playing?

Answer:
Steps for drawing the bar graph:
(i) Draw two perpendicular lines, \( OX \) (horizontal) and \( OY \) (vertical).
(ii) Draw vertical bars (rectangles) of the same width, making sure to keep equal spacing between them.
(iii) Given the scale: \( 1 \) unit length \( = 5 \) students.
Therefore, the heights of the bars will be calculated as follows:
For playing: \( 45 \div 5 = 9 \) units
For reading story books: \( 30 \div 5 = 6 \) units
For watching TV: \( 20 \div 5 = 4 \) units
For listening to music: \( 10 \div 5 = 2 \) units
For painting: \( 15 \div 5 = 3 \) units

Answer: From the bar graph, playing is the most preferred activity with \( 45 \) students. Among other activities, 'Reading story books' is preferred by \( 30 \) students, which is the highest number after playing.
In simple words: First, we draw lines and mark out the scale, with each small block meaning 5 students. Then, we make bars for each activity as tall as the number of students who like it. Looking at the finished graph, after "playing", "reading story books" is the most popular activity.

Exam Tip: When drawing bar graphs, always label both axes clearly, choose an appropriate scale, and ensure the bars have uniform width and equal spacing for better visual representation.

 

Question 2. The number of Mathematics books sold by a shopkeeper on six consecutive days is shown below:

Draw a bar graph to represent the above information choosing the scale of your choice.

Answer:
Steps for drawing the bar graph:
(i) Draw two perpendicular lines, \( OX \) (horizontal) and \( OY \) (vertical).
(ii) Draw bars (rectangles) of equal width on \( OX \), making sure they have the same spacing between them.
(iii) Taking an appropriate scale (here, \( 1 \) unit length \( = 10 \) books), we determine the heights of various bars as follows:
For Sunday: \( 65 \div 10 = 6.5 \) units
For Monday: \( 40 \div 10 = 4 \) units
For Tuesday: \( 30 \div 10 = 3 \) units
For Wednesday: \( 50 \div 10 = 5 \) units
For Thursday: \( 20 \div 10 = 2 \) units
For Friday: \( 70 \div 10 = 7 \) units

Answer: The bar graph shows the number of Mathematics books sold over six days. The highest sales happened on Friday, with \( 70 \) books, and the lowest sales were on Thursday, with \( 20 \) books. The graph helps us easily compare daily book sales.
In simple words: We make a graph with bars to show how many math books were sold each day. Each bar's height shows the number of books, using a scale where 1 unit means 10 books.

Exam Tip: When choosing a scale for a bar graph, select one that allows the largest value to fit comfortably on the axis while still showing differences between bars clearly.

 

Question 3. The following table shows the number of bicycles manufactured in a factory during the years 1998-2002. Illustrate this data using a bar graph. Choose a scale of your choice.

(a) In which year was the maximum number of bicycles manufactured?
(b) In which year was the minimum number of bicycles manufactured?

Answer:
Steps for drawing the bar graph:
(i) Draw two perpendicular lines, \( OX \) (horizontal) and \( OY \) (vertical).
(ii) Draw bars of equal width on \( OX \), ensuring they have the same spacing between them.
(iii) For determining the heights of various bars, we select an appropriate scale: \( 1 \) unit length \( = 200 \) bicycles.
Therefore, the heights of the bars will be:
For \( 1998 \): \( 800 \div 200 = 4 \) units
For \( 1999 \): \( 600 \div 200 = 3 \) units
For \( 2000 \): \( 900 \div 200 = 4.5 \) units
For \( 2001 \): \( 1100 \div 200 = 5.5 \) units
For \( 2002 \): \( 1200 \div 200 = 6 \) units

Answer: From the bar graph, we can observe the following:
(a) The maximum number of bicycles were produced in \( 2002 \), totaling \( 1200 \) bicycles.
(b) The minimum number of bicycles were produced in \( 1999 \), totaling \( 600 \) bicycles.
In simple words: The graph plainly shows that the factory made the most bikes in the year 2002, and they made the fewest bikes in 1999.

Exam Tip: When asked to identify maximum or minimum values from a bar graph, simply look for the tallest or shortest bar, respectively.

 

Question 4. The number of persons in various age groups in a town is given in the following table.

Draw a bar graph to represent the above information and answer the following questions. (take 1 unit length = 20 thousand)
(a) Which two age groups have the same population?
(b) All persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town?

Answer:
Steps for drawing the bar graph:
(i) Draw two perpendicular lines, \( OX \) (horizontal) and \( OY \) (vertical).
(ii) Draw bars of equal width on \( OX \), maintaining the same spacing between them.
(iii) Since the scale is given: \( 1 \) unit length \( = 20 \) thousand persons.
Therefore, the heights of various bars are given as:
For \( 1-14 \): \( 2,00,000 \div 20,000 = 10 \) units
For \( 15-29 \): \( 1,60,000 \div 20,000 = 8 \) units
For \( 30-44 \): \( 1,20,000 \div 20,000 = 6 \) units
For \( 45-59 \): \( 1,20,000 \div 20,000 = 6 \) units
For \( 60-74 \): \( 80,000 \div 20,000 = 4 \) units
For \( 75 \) and above: \( 40,000 \div 20,000 = 2 \) units

Answer: From the bar graph, we can find the following information:
(a) The age groups \( 30-44 \) and \( 45-59 \) both have the same population, with \( 1 \) lakh \( 20 \) thousands each.
(b) The number of senior citizens (persons aged \( 60 \) and above) are found by adding the populations of the \( 60-74 \) and \( 75 \) and above age groups:
\( 80,000 + 40,000 = 1,20,000 \)
So, there are \( 1,20,000 \) senior citizens in the town.
In simple words: The bar graph visually presents the population of various age groups. We can clearly see that two groups, 30-44 and 45-59, have the same number of people. To find the total senior citizens, we add the numbers for those aged 60 and older.

Exam Tip: Always pay attention to the specific questions asked after the graph. Some questions may require calculations using the data, while others can be answered by direct observation from the graph.