NCERT Exemplar Solutions For Class 6 Maths Chapter 9 Data Handling

Class 6 Maths Chapter 9 Data Handling

Question 1. Using tally marks, which one of the following represents the number eight:

Solution: (4): 8 can be represented as an image

Question 2. The marks (out of 0) obtained by 28 students in a Mathematics test are listed below:

8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 1 0, 1 0, 3, 4, 8, 7, 8, 9, 2,0

The number of students who obtained marks more than or equal to 5 is

1. 13
2. 15
3. 16
4. 17

Solution: (4): The number of students who obtained marks more than or equal to 5 is 17

Question 3. In question 2 above, the number of students who scored marks less than 4 is

1. 15
2. 13
3. 12
4. 10

Solution: (4): The number of students who scored marks less than 4 is 10

Read and Learn More Class 6 Maths Exemplar Solutions

Question 4. The choices of the fruits of 42 students in a class are as follows:

A,0,B,M,A,G,B,G,A,G, B,M,A,G,M,A,B,G,M,B, A,0,M,0,G,B,0,M,G,A, A,B,M,0,M,G,B,A,M,0,M,0,

where A, B, G, M, and O stand for the fruits Apple, Banana, Grapes, Mango, and Orange respectively.

Which two fruits are liked by an equal number of students?

1. A and M
2. M and B
3. B and O
4. B and G

Solution: (4): We have given two fruits Banana and Grapes, which are liked by an equal number of students i.e., 8.

Question 5. According to data from question 4, which fruit Is liked by most of the students?

1. O
2. G
3. M
4. A

Solution: (3): Mango is the only fruit liked by most students.

Question 6. In a bar graph, the width of bars may be unequal.
Solution: False

In a bar graph, bars have equal width.

Question 7. In a bar graph, bars of uniform width are drawn vertically only.
Solution: False

In a bar graph, bars of uniform width can be drawn vertically as well as horizontally.

Question 8. In a bar graph, the gap between two consecutive bars may not be the same.
Solution: False

The gap between two consecutive bars should be the same in a bar graph.

Question 9. In a bar graph, each bar (rectangle) represents only one value of the numerical data.
Solution: True

Question 10. To represent the population of different towns using a bar graph, it is convenient to take one unit length to represent one person.
Solution: False

Question 11. Pictographs and bar graphs are pictorial representations of the numerical data.
Solution: True

Question 12. An observation occurring five times in data is recorded as an image using tally marks.
Solution: False

Using tally marks, the occurrence of any observation five times can be represented as an image

Question 13. In a pictograph, if a symbol represents 50 books on a library shelf, then the symbol represents 25 books.

Solution: True

Question 14. A _______is a collection of numbers gathered to give some meaningful information.
Solution: Data

Question 15. The data can be arranged in a tabular form using_______marks.
Solution: Tally

Question 16. A_______ represents data through pictures of objects
Soluction: Pictograph

17. In a bar graph, _______ can be drawn horizontally or vertically.
Solution: Bars

Question 18. In a bar graph, bars of _______ width can be drawn horizontally or vertically with _______ spacing between them.
Solution: Uniform, Equal

Question 19. An observation occurring seven times in a data is represented as _______ using tally marks.
Solution: 

Question 20. In a pictograph, if a symbol represents 20 flowers in a basket then stands for _______ flowers.
Solution: 60

Question 21. On the scale of 1 unit length = 10 crores, the bar of length 6 units will represent _______ crore, and of _______units will represent 75 crores.
Solution: 60, 7.5

Question 22. In an examination, the grades achieved by 30 students of a class are given below. Arrange these grades in a table using tally marks:

B, C, C, E, A, C, B, B, D, D, D, D, B, C, C, C, A, C, B, E, A, D, C, B, E, C, B, E, C, D

Solution:

Question 23. The number of two-wheelers owned individually by each of the 50 families is listed below. Make a table using tally marks.

1,1, 2, .1,1, 1,2, 1,2, 1,0, 1,1, 2, 3,1,2, 1,1,2, 1, 2, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 1, 2, 1,1, 1,1, 2, 3, 2,1,1

Find the number of families having two or more, two-wheelers

Solution:

So, 14 + 4 + 1 = 19 families have two or more, two-wheelers

Question 24. The lengths in centimeters (to the nearest centimeter) of 30 carrots are given as follows:

15, 22, 21, 20, 22,15, 15, 20, 20,15, 20, 18, 20, 22, 21, 20, 21, 18, 21, 18, 20, 18, 21, 18, 22, 20, 15,21,18, 20

Arrange the data given above in a table using tally marks and answer the following questions.

1. What is the number of carrots which have a length of more than 20 cm?
2. Which length of the carrots occur the maximum number of times? The minimum number of times?

Solution:

1. The number of carrots that have a length of more than 20 cm is 6 + 4 = 10.
2. The carrots of length 20 cm occur a maximum number of times and the carrots of length 22 cm occur a minimum number of times

Question 25. Thirty students were interviewed to find out what they wanted to be in the future. Their responses are listed below:

doctor, engineer, doctor, pilot, officer, doctor, engineer, doctor, pilot, officer, pilot, engineer, officer, pilot, doctor, engineer, pilot, officer, doctor, officer, doctor, pilot, engineer, doctor, pilot, officer, doctor, pilot, doctor, engineer.

Arrange the data in a table using tally marks.

Solution:

Question 26. Following are the choices of games for 40 students of Class 6:

football, cricket, football, kho-kho, hockey, cricket, hockey, kho-kho, tennis, tennis, cricket, football, football, hockey, kho-kho, football, cricket, tennis, football, hockey, khokho, football, cricket, cricket, football, hockey, kho-kho, tennis, football, hockey, cricket, football, hockey, cricket, football, kho-kho, football, cricket, hockey, football.

Arrange the choices of games in a table using tally marks.

1. Which game is liked by most of the students?
2. Which game is liked by the minimum number of students?

Solution: 1.

1. Football is liked by most of the students.
2. Tennis is liked by a minimum number of students.

Question 27. Fill in the blanks in the following table which represents the shirt size of 40 students of a school.

Solution:

Question 28. The following pictograph represents some surnames of people listed in the telephone directory of a city.

Observe the pictograph and answer the following questions:

1. How many people have the surname ‘Roy’?
2. Which surname appears the maximum number of times in the telephone directory?
3. Which surname appears the least number of times in the directory?
4. Which two surnames appear an equal number of times?

Solution:

1. 400 people have the surname ‘Roy’.
2. The surname ‘Patel’ appears the maximum number of times in the telephone directory.
3. The surname ‘Saikia’ appears the least number of times in the telephone directory.
4. The surnames ‘Rao’ and ‘Roy’ appear an equal number of times.

Question 29. Students of Class 6 in a school were given a task to count the number of articles made of different materials in the school. The information collected by them is represented as follows:

Observe the pictograph and answer the following questions:

1. Which material is used in a maximum number of articles?
2. Which material is used in a minimum number of articles?
3. Which material is used in exactly half the number of articles as those made up of metal?
4. What is the total number of articles counted by the students?

Solution:

1. Metal is used in a maximum number of articles.
2. Glass is used in the minimum number of articles.
3. Rubber is used in exactly half the number of articles as those made up of metal.
4. The total number of articles counted by the students is 160.

Question 30. The number of scouts in a school is depicted by the following pictograph:

Observe the pictograph and answer the following questions:

1. Which class has the minimum number of scouts?
2. Which class has the maximum number of scouts?
3. How many scouts are there in Class 6?
4. Which class has exactly four times the scouts as that of Class X?
5. What is the total number of scouts in the Classes 6 to 10?

Solution:

1. Class 10 has a minimum number of scouts.
2. Class 8 has a maximum number of scouts.
3. There are 40 scouts in Class 6.
4. Class 6 has exactly four times the scouts as that of Class 10.
5. Total number of scouts in the Classes 6 to 10 is 160.

Question 31. A survey was carried out in a certain school to find out the popular school subjects among students of Classes VI to VIII. The data in this regard is displayed as a pictograph given below:

1. Which subject is most popular among the students?
2. How many students like Mathematics?
3. Find the number of students who like subjects other than Mathematics and Science.

Solution:

1. Hindi is the most popular subject among the students.
2. 175 students like Mathematics.
3. A total of 200 + 150 + 75 = 425 students are there who like subjects other than Mathematics and Science.

Question 32. The following pictograph depicts the information about the areas in sq km (to the nearest hundred) of some districts of Chhattisgarh State:

1. What is the area of the Koria district?
2. Which two districts have the same area?
3. How many districts have an area of more than 5000 square kilometers?

Solution:

1. The area of Koria district is 6000 sq km.
2. Raigarh and Jashpur districts have the same area of 6500 sq km.
3. 4 districts have an area of more than 5000 square kilometers and they are Raigarh, Rajnandgaon, Koria, and Jashpur

Question 33. The number of bottles of cold drinks sold by a shopkeeper on six consecutive days is as follows:

Prepare a pictograph of the data using one symbol to represent 50 bottles.

Solution:

Question 34. The following table gives information about the circulation of newspapers (dailies) in a town in five languages.

Prepare a pictograph of the above data, using a symbol of your choice, each representing 1000 newspapers.

Solution:

Question 35. Annual expenditure of a company in the year 2007-2008 is given below:

Prepare a pictograph of the above data using an appropriate symbol to represent ₹ 10 lakh.

Solution:

Question 36. The houses following (out ofbar100) graphing a showdown using the number of different types of fuels for cooking.

Read the bar graph and answer the following questions:

1. Which fuel is used in the maximum number of houses?
2. How many houses are using coal as fuel?
3. Suppose that the total number of houses in the town is ₹ 1 lakh. From the above graph estimate the number of houses using electricity.

Solution:

1. LPG is used in a maximum number of houses.
2. 10 houses are using coal as fuel.
3. Since there are 5 houses using electricity out of 100. Therefore, out of ₹ 1 lakh, the electricity will be used by \(\frac{5}{100} \times 100000\) = 5000 houses.

Question 37. The following bar graph represents the data for different sizes of shoes worn by the students in a school. Read the graph and answer the following questions.

1. Find the number of students whose shoe sizes have been collected.
2. What is the number of students wearing shoe size 6?
3. What are the different sizes of the shoes worn by the students?
4. Which shoe size is worn by the maximum number of students?
5. Which shoe size is worn by the minimum number of students?
6. State whether true or false: The total number of students wearing shoe sizes 5 and 8 is the same as the number of students wearing shoe size 6.

Solution:

1. The total number of students whose shoe sizes have been collected = 250 + 200 + 300 + 400 + 150 = 1300
2. The number of students wearing shoe size 6 is 300.
3. The different sizes of the shoes worn by the students are 4, 5, 6, 7, and 8.
4. The shoe size 7 is worn by the maximum number of students.
5. The shoe size 8 is worn by the minimum number of students.
6. False: Since the number of students wearing shoe sizes 5 and 8 is 350 and the number of students wearing shoe size 6 is 300.

Question 38. The following graph gives information about the number of railway tickets sold for different cities on a railway ticket counter between 6.00 am to 10.00 am. Read the bar graph and answer the following questions.

1. How many tickets were sold in all?
2. For which city were the maximum number of tickets sold?
3. For which city were the minimum number of tickets sold?
4. Name the cities for which the number of tickets sold is more than 20.
5. Fill in the blanks: The number of tickets sold for Delhi and Jaipur together exceeds the total number of tickets sold for Patna and Chennai by________.

Solution:

1. Total number of tickets sold = 80 + 50 + 100 + 20 + 45 = 295
2. The maximum number of tickets were sold for Delhi.
3. The minimum number of tickets were sold for Chennai.
4. The cities for which the number of tickets sold is more than 20 are as follows: Patna, Jaipur, Delhi, and Guwahati.
5. 50: Number of tickets sold for Delhi and Jaipur together = 100 + 50 = 150.

• Number of tickets sold for Patna and Chennai together = 80 + 20 = 100
• Therefore, tickets sold for Delhi and Jaipur exceed the tickets sold for Patna and Chennai by 150- 100 = 50.

Question 39. The bar graph given below represents the approximate length (in kilometers) of some National Highways in India. Study the bar graph and answer the following questions:

1. Which National Highway (N.H.) is the longest among the above?
2. Which National Highway is the shortest among the above?
3. What is the length of National Highway 9?
4. Length of which National Highway is about three times the National Highway l0?

Solution:

1. The longest National Highway is N.H. 2.
2. The shortest National Highway is N.H. 10.
3. The length of National Highway 9 is 900 km.
4. Length ofNational Highway 10 = 450km Length ofNational Highway 8 = 1400km

So, the length of National Highway 8 is about three times the of National Highway 10

Question 40. The bar graph given below represents the circulation of newspapers in different languages in a town. Study the bar graph and answer the following questions:

What is the circulation of English newspapers?

Name the two languages in which the circulation of newspapers is the same.

By how much is the circulation of newspapers in Hindi more than the newspaper in Bengali?

Solution:

1. The circulation of English newspapers is 1000.
2. In Bengali and Marathi languages the circulation of newspapers is the same.
3. The circulation of newspapers in Hindi is more than the newspaper in Bengali by 1400-600 = 800.

Question 41. Read the bar graph given below and answer the following questions:

1. What information is given by the bar graph?
2. In which year is the number of students maximum?
3. In which year is the number of students twice that of 2001 -02?
4. In which year did the number of students decrease as compared to the previous year?
5. In which year is the increase in number of students maximum as compared to the previous year?

Solution:

1. The given bar graph shows the number of students in different academic years.
2. In the year 2005-06, the number of students is maximum.
3. Since number of students in 2001-02 is150 and number of students in 2004-05 is 300. So, in the year 2004-05, the number of students is twice that of 2001-02.
4. In the year 2003-04, the number of students decreased as compared to the previous year.
5. The year is 2004-05in which the increase in number of students is maximum as compared to the previous year

Question 42. The lengths in km (rounded to the nearest hundred) of some major rivers of India are given below:

Draw a bar graph to represent the above information.

Solution:

Question 43. The number of ATMs of different banks in a city is shown below:

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

Solution:

Question 44. Number of mobile phone users in various age groups in a city is listed below:

Draw a bar graph to represent the above information.

Solution:

Question 45. The following table gives the number of vehicles passing through a toll gate, every hour from 8.00 am. to 1.00 pm:

Draw a bar graph representing the above data.

Solution:

Question 46. The following table represents the income of a Gram Panchayat from different sources in a particular year:

Draw a bar graph to represent the above information.

Solution:

Question 47. The following table gives the data on several schools (stage-wise) in a country in the year 2002.

Draw a bar graph to represent the above data:

Solution:

Question 48. Home appliances sold by a shop in one month are given as below:

Draw a bar graph to represent the above information.

Solution:

Question 49. In a botanical garden, the number of different types of plants are found as follows:

Draw a bar graph to represent the above information and answer the following questions:

1. Which type of plant is the maximum in number in the garden?
2. Which type of plant is the minimum in number in the garden?

Solution:

1. The tree is the maximum in number in the garden.
2. Creeper is the minimum in number in the garden.

Question 50. Prepare a bar graph of the data given in question 28.

Solution:

Question 51. Refer to question 39. Prepare a pictograph of the data by taking a suitable symbol to represent 200 kilometers.
Solution:

Question 52. Prepare a pictograph of the information given in question 38.
Solution:

Question 53. Refer to question 23. Prepare a bar graph of the data.
Solution:

Question 54. The following table shows the area of the land on which different crops were grown.

Prepare a pictograph by choosing a suitable symbol to represent 10 million hectares.

Solution:

Question 55. Refer to question 54. Prepare a bar graph of the data.
Solution: