GSEB Class 7 Maths Solutions Chapter 3 Data Handling Exercise 3.3

 

Question 1. Use the following bar graph to answer the following questions:

Answer:
(a) The bar showing cats is the tallest, so the cat is the most popular pet.
(b) 8 students have a dog as their pet.
In simple words: To find the most popular pet, look for the tallest bar. To find how many children have dogs, find the "Dogs" bar and read its height on the "Students" scale.

Exam Tip: When reading bar graphs, always check the labels on both the X-axis and Y-axis to understand what data each bar represents.

 

Question 2. Read the following bar graph which shows the number of books sold by a booksstore during five consecutive years and answer the following questions:
(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books soldiAbout 225 books soldi?
(iii) In which years were fewer than 250 books soldi?
(iv) Can you explain how you would estimate the number of books sold in 1989?

Answer:
(i) In 1989, approximately 180 books were sold. In 1990, about 475 books were sold. In 1992, around 225 books were sold.
(ii) Around 475 books were sold in 1990, and about 225 books were sold in 1992.
(iii) Fewer than 250 books were sold in 1989 and 1992.
(iv) The bar's height for 1989 is a little below the 200 books line. So, we can estimate that around 180 books were sold in 1989.
In simple words: Look at each year's bar and read its top value on the "Number of books" scale. If the bar is between two numbers, make your best guess.

Exam Tip: When estimating values from a bar graph, pay attention to the scale and how close the bar top is to the nearest grid line.

 

Question 3. Number of children in six different classes are given below. Represent the data on the bat-graph.

Answer:
(a) The largest data value here is 135, which is less than 140. So, we can pick a scale from 0 to 140 that is neither too long nor too short. By selecting a scale where 1 unit equals 10 students and placing classes along the x-axis, we create the bar graph as shown below:

(b)
(i) The Fifth class has the highest number of children, which is 135 students. The Tenth class has the lowest number of children, which is 80 students.
(ii) The number of children in sixth class is 120. The number of children in eighth class is 100.
Therefore, the necessary ratio is \( \frac { 120 }{ 100 } = \frac { 6 }{ 5 } = 6:5 \).
In simple words: First, select a good range for your graph's number scale. Then, draw bars for each class, making their height match the number of children. The tallest bar shows the most children, and the shortest shows the fewest. To find a ratio, divide the number of children in one class by the number in another and simplify the fraction.

Exam Tip: When setting a scale for a bar graph, make sure it covers all your data points without making the graph too stretched or squashed. Always simplify ratios to their lowest terms.

 

Question 4. The performance of a student in 1st Term and 2nd Term is given. Draw a double bar graph choosing appropriate scale and answer the following:

(i) In which subject, has the child improved his performance the most?
(ii) In which subject is the improvement the least?
(iii) Has the performance gone down in any subject?
Answer:
The requested double bar graph is shown below:
(i) Improvement in marks:
In English = \( 70 - 67 = 3 \)
In Hindi = \( 65 - 72 = -7 \)
In Maths = \( 95 - 88 = 7 \)
In Science = \( 85 - 81 = 4 \)
In Social Science = \( 75 - 73 = 2 \)
Clearly, the performance has improved the most in Maths.
(ii) The performance in Social Science shows the least improvement (difference of 2 marks).
(iii) Yes, the performance in Hindi has decreased.
In simple words: To see who improved most, look at the difference between the first and second term bars for each subject. The biggest positive difference means the most improvement. If the second bar is shorter than the first, the performance went down.

Exam Tip: For double bar graphs, make sure to clearly distinguish between the two sets of data (e.g., different colors, clear legend) and correctly interpret the difference or comparison between them.

 

Question 5. Consider this data collected from a survey of a colony.

(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(ii) Which sport is most popular?
(iii) Which is more preferred, watching or participating in sports?
Answer:
(i) The necessary 'double bar graph' is shown below:
From the bar graph, we can conclude that the people in the colony like cricket the most and athletics the least.
(ii) The most popular sport is cricket.
(iii) Watching sports is more popular than actually taking part in sports.
In simple words: Create a graph with two bars for each sport: one for watching and one for playing. Use a scale that fits all numbers. By looking at the bars, you can easily tell which sport is loved most, which is least popular, and if more people prefer to watch or participate.

Exam Tip: For a double bar graph, ensure you clearly label each bar type (e.g., 'Watching' vs. 'Participating') and use different colors or patterns to make them easy to distinguish. Always summarize the key findings or trends after drawing the graph.

 

Question 6. Plot a double bar graph using the data and answer the following questions:
(i) Which city has the largest difference in the minimum and maximum temperature on the given date?
(ii) Which is the hottest city and which is the coldest city?
(iii) Name two cities where maximum temperature of one was less than the minimum temperature of the other.
(iv) Name the city which has the least difference between its minimum and the maximum temperature.

Table 3.1, Page 57 NCERT Textbook
Temperature of cities as on 20.06.2006

Answer:
Plotting a double bar graph, we obtain:

From the double bar graph, we have:

(i) Clearly, Jammu has the largest difference in the minimum and maximum temperature on the specified date.
(ii) Jammu is the warmest city, and Bangalore is the coolest city.
(iii) Bangalore and Ahmedabad (or Jaipur) are two cities where the maximum temperature of one was lower than the minimum temperature of the other.
(iv) Mumbai has the smallest difference between its maximum and minimum temperature.
In simple words: Draw a graph with two bars for each city, showing maximum and minimum temperatures. Calculate the temperature difference for each city to find the largest and smallest gaps. The tallest maximum temperature bar indicates the hottest city, and the shortest minimum temperature bar shows the coldest. Then, compare temperatures between cities as asked.

Exam Tip: When dealing with temperature data, clearly label maximum and minimum values. Calculating the difference for each entry first can simplify answering questions about the largest or smallest variations.