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NCERT Solutions for Class 6 Maths

Chapter 9 Data Handling

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.

8 I 3 7 6 5 5 4 4 2
4 9 5 3 7 I 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6

(a) Find how many students obtained marks equal to or more than 7.

(b) How many students obtained marks below 4?

Solution.

(a) 5 + 4 + 3=12 students obtained marks equal to or more than 7.

(b) 3 + 3 + 2 = 8 students obtained marks below 4.

Question 2.

Following is the choice of sweets of 30 students of Class VI

Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo.

(a) Arrange the names of sweets in a table using tally marks.

(b) Which sweet is preferred by most of the students?

Solution.

(a)

(b) Ladoo is preferred by most of the students.

1 3 5 6 6 3 5 4 1 6
2 5 3 4 6 1 5 5 6 1
1 2 2 3 5 2 4 5 5 6
5 1 6 2 3 5 2 4 1 5

Question 3.

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 limes.

Solution.

(a) The number that appeared the minimum number of times is 4.

(b) The number that appeared the maximum number of times is 5.

(c) The numbers that appeared an equal number of times are 1 and 6.

Question 4.

Following pictograph shows the number of tractors in five villages:

Observe the pictograph and answers 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?

Solution.

(i) Village D has the minimum number of tractors.

(ii) Village C has the maximum number of tractors.

(iii) Village C has 8-5 = 3 more tractors as compared to village B.

(iv) Total number of tractors in all the five 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 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 VII class?

Solution.

(a) Class VIII has the minimum no. of girl students.

(b) No! the number of girls in class VI is not less than the number of girls in class V.

(c) Number of girls in class VII – 3 x 4 = 12.

Question 6.

The sale of electric bulbs on different days of a week is shown below:

What can we conclude from the said pictograph?

Observe the pictograph and answer the following questions:

(a) How many bulbs were sold on Friday?

(b) On which day the maximum number of bulbs were sold?

(c) If one bulb was sold at the rate off 10, what was the total sale on Sunday?

(d) Can you find out the total sale of the week?

(e) If one big carton can hold 9 bulbs, how many cartons were needed in the given week?

Solution.

(a) Number of bulbs sold on Friday = 7×2 = 14.

(b) The maximum number of bulbs were sold on Sunday.

(c) Number of bulbs sold on Sunday

= 9 x 2=18.

∴ Total sale on Sunday

= Rs.18 x 10 = Rs. 180.

(d) Total number of bulbs sold in the week

= (6 + 8 + 4 + 5 + 7 + 4 + 9) x 2

= 43 x 2 = 86.

Hence, 10 cartons were needed in the given week.

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 number of baskets are planning to buy a godown for the next season. Can you name them?

Solution.

(a) Martin sold the maximum number of baskets.

(b) 7 x 100 = 700 fruit baskets were sold by Anwar.

(c) Yes! Anwar. Martin and Ranjit Singh are planning to buy a godown for the next season.

Exercise 9.2

Question 1.

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:

(i) How many symbols represent animals of village E?

(ii) Which village has the maximum number of animals?

(iii) Which village has more animals: Village A or village C?

Solution.

(i) 6 symbols represent animals of village E.

(ii) Village B has the maximum number of animals.

(iii) Village C has more animals than village A.

Question 2.

The total number of students in a school in different years is shown in the following table:

Year Number of students
1996 400
1998 535
2000 472
2002 600
2004 623

A. Prepare a pictograph of students using one symbol to 

represent 100 students and answer the following questions:

(i) How many symbols represent total number of students in the year 2002?

(ii) 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?

Solution.

(A)

(i) 6 symbols represent total number of students in the year 2002.

(ii) 0 5 complete and 1 incomplete symbols represent total number of students for the year 1998.

(B)

Pictograph B is more informative because it gives better approximations.

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 production maximum?

(b) the wheat production minimum?

Solution.

(a) The wheat production was maximum in the year 2002.

(b) The wheat production was minimum in the year 1998.

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 a number of shills?

(c) On which day were the maximum number of shirts sold? How many shirts were sold on that day?

(d) On which day were the minimum number of shirts sold?

(e) How many shirts were sold on Thursday?

Solution.

(a) This bar graph shows the number of shirts sold from Monday to Saturday.

(b) 1 unit = 5 shirts

(c) Saturday, 60

(d) Tuesday

(e) 35 shirts.

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

Solution.

(a) This bar graph shows the marks obtained by Aziz in different subjects.

(b) Hindi

(c) Social Studies

(d) Hindi-80, English-60, Mathematics-70, Science-50 and 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:

Preferred activity Number of students
Playing 45
Reading story books 30
Watching T.V. 20
Listening to music 10
Painting 15

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?

Solution.

(i) Draw two perpendicular lines—one vertical and one horizontal.

(ii) Along horizontal line mark the “Preferred activity” and along vertical line mark the “No. of students”

(iii) Take bars of same width keeping the uniform gap between them.

(iv) Take scale of 1 unit length = 5 students along the vertical line and then mark the corresponding values.

(v) Calculate the heights of the bars for various activities preferred as shown below :

Playing                      :  45÷5= 9 units

Reading story books :  30÷5= 6 units

Watching T.V.           :   20÷4 =4 units

Listening to Music    :   10÷5= 2 units

Painting                    :   15÷5=3 units

(vi) Now draw various bars.

The activity “Reading story books” is preferred by most of the students other than playing.

Question 2.

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

Days Sunday Monday Tuesday Wednesday Thursday Friday
Number of books sold 65 40 30 50 20 70

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

Solution.

(i) Draw two perpendicular lines—one vertical and one horizontal.

(ii) Along horizontal line mark the “days” and along vertical line mark the “number of books sold.”

(iii) Take bars of same width keeping the uniform gap between them.

(iv) Take scale of 1 unit length = 5 books along the vertical line and mark the corresponding values.

(v) Calculate the heights of the bars for various days as shown below:

Sunday   : 65÷5=13 units

Monday  : 40÷5=8 units

Tuesday  : 30÷5=6 units

Wednesday : 50÷5=10 units

Thursday : 20÷5=4 units

Friday : 70÷5=14 units

(vi) Now draw various bars.

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.

 Year Number of bicycles manufactured
1998 800
1999 600
2000 900
2001 1100
2002 1200

(i) In which year was the maximum number of bicycles manufactured?

(ii) In which year was the minimum number of bicycles manufactured?

Solution.

Steps for drawing a bar graph

(i) Draw two perpendicular lines — one vertical and one horizontal.

(ii) Along horizontal line marks the Year and along vertical line mark the “No. of bicycles manufactured”.

(iii) Take bars of same width keeping uniform gaps between them.

(iv) Take scale of 1 unit length = 100 bicycles along the vertical line and then mark the corresponding values.

(v) Calculate the heights of the bars for various years as shown below:

1998: 800÷100=8 units

1999: 600÷100=6 units

2000: 900÷100=9 units

2001: 1100÷100=11 units

2002: 1200÷100=12 units

(vi) Now draw various bars.

(i) The maximum number of bicycles were manufactured in the year 2002.

(ii) The minimum number of bicycles were manufactured in the year 1999.

Question 4.

A number of persons in various age groups in a town is given in the following table:

Age group Number of persons
1-14 2 lakhs
15-29 1 lakh 60 thousand
30-44 1 lakh 20 thousand
45-59 1 lakh 20 thousand
60-74 80 thousand
75 and above 40 thousand

Draw a bar graph to represent the above information and answer the following questions. (take 1 unit length = 20 thousands):

(i) Which two age groups have the same population?

(ii) All persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town?

Solution.

(i) Draw two perpendicular lines — one vertical and one horizontal.

(ii) Along horizontal line mark the “Age group” and along vertical line mark the “Number of persons”.

(iii) Take bars of same width keeping uniform gap between them.

(iv) Take scale of 1 unit length = 20 thousand along the vertical line and then mark the corresponding values.

(v) Calculate the heights of the bars for various of groups as shown below:

1- 14 : 20000020000 =10 units

15- 29 : 16000020000 = 8 units

30- 44 : 12000020000 = 6 units

45- 59 : 12000020000 = 6 units

60- 74 : 8000020000 = 4 units

75 and above : 4000020000 = 2 units

(vi) Now draw various bars.

(i) The two age-groups 30-44 and 45-59 have the same population.

(ii) Number of senior citizens in the town

= 80000 + 40000

= 120000

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