Data Handling
Class 6th Mathematics CBSE Solution
- In a Mathematics test, the following marks were obtained by 40 students. Arrange…
- Following is the choice of sweets of 30 students of Class VI : Ladu, Barfi,…
- Catherine threw a die 40 times and noted the number appearing each time as shown…
- Following pictograph shows the number of tractors in 5 villages. Observe the…
- The number of girl students in each class of a co-educational middle school is…
- The sale of electric bulbs on different days of a week is shown below: What can…
- In a village, six fruit merchants sold the following number of fruit baskets in…
- A total number of animals in five villages are as follows: Village A: 80 Village…
- A total number of students of a school in different years is shown in the…
- The bar graph given alongside shows the amount of wheat purchased by the…
- Observe this bar graph which is showing the sale of shirts in a ready made shop…
- Observe this bar graph which shows the marks obtained by Aziz in half-yearly…
- A survey of 120 school students was done to find which activity they prefer to…
- The number of Mathematics books sold by a shopkeeper on six consecutive days is…
- Following table shows the number of bicycles manufactured in a factory during…
- Number of persons in various age groups in a town is given in the following…
Exercise 9.1
Question 1.In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.
(a) Find how many students obtained marks equal to or more than 7?
(b) How many students obtained marks below 4?
Answer:
By observing the above-given marks of 40 students, we can construct the table as follows:
(a) Students who have scored marks equal to and more than 7 = No. of students with marks 7 +No. of students with marks 8 + No. of students with marks 9
5 + 4 + 3
= 12
(b) Students who have scored marks less than 4 =No. of students with marks 1 + No. of students with marks 2 + No. of students with marks 3
2 + 3 + 3
= 8
Question 2.
Following is the choice of sweets of 30 students of Class VI :
Ladu, Barfi, Ladu, Jalebi, Ladu, Rasgulla,
Jalebi, Ladu, Barfi, Rasgulla, Ladu, Jalebi
Jalebi, Rasgulla, Ladu, Radgulla, Jalebi, Ladu
Rasgulla, ladu, Ladu, barfi, Rasgulla, Rasgulla,
Jalebi, Rasgulla, Ladu, Rasgulla, Jalebi, Ladu
(a) Arrange the names of sweets in a table using tally marks
(b) Which sweet is preferred by most of the students?
Answer:
(a) By observing the choices of given 30 students, we can construct a table as follows:
(b) From the above table, it is clear that Ladoo is the most preferred sweet as most number of students preferred the sweet ladoo
Question 3.
Catherine threw a die 40 times and noted the number appearing each time as shown below:
Make a table and enter the data using tally marks
Find the number that appeared
(a) The minimum number of times
(b) The maximum number of times
(c) Find those numbers that appear an equal number of times
Answer:
Table for the above-given data is as follows:
(a) From the above table, the number which appeared the minimum number of times is 4
(b) From the above table, the number which appeared the maximum number of times is 5
(c) From the above table, there are two numbers which appear for the same number of times and these are 1 and 6
Question 4.
Following pictograph shows the number of tractors in 5 villages.
Observe the pictograph and answer the following questions:
(i) Which village has the minimum number of tractors?
(ii) Which village has the maximum number of tractors?
(iii) How many more tractors village C has as compared to village B?
(iv) What is the total number of tractors in all the five villages?
Answer:
(i) From the above pictograph, it is clear Village D has the minimum number of tractors as this village has only 3 tractors
(ii) From the above pictograph, it is clear Village C has the maximum number of tractors as this village has 8 tractors
(iii) From the above pictograph,
Number of more tractors that village C has as compared to B = 8 – 5 = 3
(iv) From the above pictograph,
Total number of tractors in all given villages = 6 + 5 + 8 + 3 + 6
= 28
Question 5.
The number of girl students in each class of a co-educational middle school is depicted by the following pictograph.
Observe this pictograph and answer the following questions:
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) How many girls are there in Class VII?
Answer:
From the above table, it is clear:
(a) From the above table, it is clear, class VIII has the minimum number of girls i.e. 6
(b) No, class VI has more number of girls than class V. Clearly, in class V and VI there are 10 and 16 girls respectively.
(c) From the above-given table,
In class VII there are total 12 girls
Question 6.
The sale of electric bulbs on different days of a week is shown below:
What can we conclude from the above pictograph?
(a) How many bulbs were sold on Friday?
(b) On which day were the maximum number of bulbs sold?
(c) On which of the days same number of bulbs were sold?
(d) On which of the days minimum number of bulbs were sold?
(e) If one big carton can hold 9 bulbs. How many cartons were needed in the given week ?
Answer:
From the above-given pictograph, we can conclude following:
a) Firstly, there are following number of bulbs on different days of the week:
b) From the given pictograph and above table, we can conclude that maximum number of bulbs were sold on Sunday, i.e. 18
c) From the above-given table, equal number of bulbs were sold on Wednesday and Saturday i.e. 8
d) From the above-given table, minimum number of bulbs were sold on Wednesday and Saturday i.e. 8
e) From the above given table,
Total number of bulbs sold in a week = 12 + 16 + 8 + 10 + 14 + 8 + 18
= 86
9 bulbs can be in = 1 carton
1 bulb can be in = 
86 bulbs can be in = 
cartons
As number of cartons cannot be in decimal.
So 10 cartons will be needed.
Question 7.
In a village, six fruit merchants sold the following number of fruit baskets in a particular season:
Observe this pictograph and answer the following questions:
(a) Which merchant sold the maximum number of baskets?
(b) How many fruit baskets were sold by Anwar?
(c) The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?
Answer:
From the above-given pictograph following table is constructed:
(a) From the above-given table, it is clear Martin sold maximum number of baskets i.e. 950
(b) Total number of fruit baskets sold by Anwar is 700
(c) The merchants who have sold more than 600 baskets are Anwar, Martin and Ranjit. Therefore, they are planning to buy a godown for the next season
Exercise 9.2
Question 1.A total number of animals in five villages are as follows:
Village A: 80
Village B: 120
Village C: 90
Village D: 40
Village E: 60
Prepare a pictograph of these animals using one symbol ⊗ to represent 10 animals and answer the following questions:
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village have more animals: village A or village C?
Answer:
We can prepare the pictograph of the given data as follows:
(a) Here,
We know that,
⊗ = 10 animals
And, it is given that, Village E has 60 animals
Hence, 6 symbols (⊗) will represent the animals of village E
(b) We can see that,
Maximum numbers of symbols (⊗) are there in the section of village B
And,
⊗ = 10 animals
Hence, Village B has a maximum number of animals.
It has 10 × 12 = 120 animals.
(c) We can observe that,
Village A has 8 symbols (⊗)
And, Village C has 9 symbols (⊗)
Now, we know that,
⊗ = 10 animals
Therefore, Village A has 80 animals
And, Village C has 90 animals
Clearly, village C has more animals in it.
Question 2.
A total number of students of a school in different years is shown in the following table:
A. Prepare a pictograph of students using one symbol 
to represent 100 students and answer the following questions:
(a) How many symbols represent total number of students in the year 2002?
(b) How many symbols represent total number of students for the year 1998?
B. Prepare another pictograph of students using any other symbol each representing 50 students. Which pictograph do you find more informative?
Answer:
(A) We can prepare the pictograph of the given data as follows:
(a) Here,
We know that,
= 100 students
And, it is given that, In the year 2002, there were 600 students
Hence,
6 symbols 
will represent the students of the year 2002
(b) Here,
We know that,
= 100 students
And, it is given that, in the year 1998, there were 535 students
Hence,
5 complete and one incomplete symbol will represent the students of the year 1998.
(B)
Hence,
We can observe that,
The second pictograph is more informative
Exercise 9.3
Question 1.The bar graph given alongside shows the amount of wheat purchased by the government during the years 1998-2002.
Read the bar graph and write down your observations. In which year was
(a) The wheat purchased maximum?
(b) In which year was the wheat purchased minimum?
Answer:
(a) We can clearly see that, the year in which there was a maximum purchase of wheat was the year 2002 with a purchase of 30 thousand tons.
(b) We can clearly see that, the year in which there was a least purchase of wheat was the year 1998 with a purchase of 15 thousand tons.
Question 2.
Observe this bar graph which is showing the sale of shirts in a ready made shop from Monday to Saturday.
Now answer the following questions:
(a) What information does the above bar graph give?
(b) What is the scale chosen on the horizontal line representing number of shirts?
(c) On which day was the maximum number of shirts sold? How many shirts were dols on that day?
(d) On which day was the minimum number of shirts sold?
(e) How many shirts were sold on Thursday?
Answer:
The parts of the questions are solved below:
(a) The bar graph represents the number of shirts sold from Monday to Saturday.
(b) The scale of the horizontal line representing the number of shirts is chosen as:
1 unit = 5 shirts
(c) From the given bar graph we can observe that,
The maximum shirts were sold on Saturday with a total number of 60 shirts.
(d) From the given bar graph we can observe that,
The minimum shirts were sold on Tuesday with a total number of 10 shirts.
(e) 35 shirts were sold on Thursday.
Question 3.
Observe this bar graph which shows the marks obtained by Aziz in half-yearly examination in different subjects
Answer the given questions:
(a) What information does the bar graph give?
(b) Name the subject in which Aziz scored maximum marks.
(c) Name the subject in which he has scored minimum marks.
(d) State the name of the subjects and marks obtained in each of them
Answer:
The various parts of the question are solved below:
(a) We can clearly observe that,
The given bar graph shows the marks obtained by Aziz in various subjects.
(b) The maximum marks were scored by Aziz in the subject of Hindi.
He scored 80 marks in Hindi.
(c) The least marks were scored by Aziz in the subject of Social Studies.
He scored 40 marks in Social Studies.
(d) The name of the subject with its respective marks are listed below:
Hindi = 80
English = 60
Maths = 70
Science = 50
Social studies = 40
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 scale of 1 unit length = 5 students.
Which activity is preferred by most of the students other than playing?
Answer:
According to the question,
We will take a scale of 1 unit length = 5 units
And hence,
We will draw the graph based on the above given data as follows:
We can clearly observe that,
The most preferred activity by the students after playing is reading story books.
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:
According to the question,
By taking a scale of 1 unit = 10 books, a bar graph of the above-given data can be constructed as follows:
Question 3.
Following table shows the number of bicycles manufactured in a factory during the years 1998 to 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:
According to the question,
By taking a scale of 1 unit = 100 bicycles, a bar graph of the above-given data can be constructed as follows:
(a) We can see that,
The maximum number of bicycles were manufactured in the year 2002.
A total of 1200 bicycles were manufactured.
(b) We can see that,
The minimum number of bicycles were manufactured in the year 2001.
A total of 600 bicycles were manufactured
Question 4.
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 thousands)
(a) Which two age groups have 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:
According to the question,
By taking a scale of 1 unit = 20 thousands, a bar graph of the above-given data can be constructed as follows:
(a) We can clearly observe that,
The age groups in which the population is same are 30 – 44 and 45 – 59.
(b) We know that,
The senior citizens are the people that are either from the age group of 60 – 74 or from the age group of 75 and above.
Hence,
We can calculate the number of senior citizens as follows:
Total no. of senior citizen = 80,000 + 40,000
= 1,20,000