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Page No 42:

Question 1:

Choose the correct answer.
The height of a rectangle in a histogram shows the
(a) Width of the class
(b) Upper limit of the class
(c) Lower limit of the class
(d) Frequency of the class

Answer:

The height of a rectangle shows the frequency of the class.

Hence, the correct answer is option D.

Page No 42:

Question 2:

Choose the correct answer.
A geometric representation showing the relationship between a whole and its parts is a
(a) Pie chart
(b) Histogram
(c) Bar graph
(d) Pictograph

Answer:

A geometric representation showing the relationship between a whole and its parts is a pie chart.

Hence, the correct answer is option A.

Page No 42:

Question 3:

Choose the correct answer.
3. In a pie chart, the total angle at the centre of the circle is
(a) 180°
(b) 360°
(c) 270°
(d) 90°

Answer:

The total angle at the centre of the circle is 360º.



Hence, the correct answer is option B.

Page No 42:

Question 4:

Choose the correct answer.
The range of the data 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 is
(a) 26
(b) 30
(c) 41
(d) 61

Answer:

Given: 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 
Here, 
Maximum Value = 61
Minimum Value = 20

∴ Range of the data = Maximum Value – Minimum Value
                              = 61 – 20
                              = 41

Hence, the correct answer is option C.

Page No 42:

Question 5:

Choose the correct answer.
Which of the following is not a random experiment?
(a) Tossing a coin
(b) Rolling a dice
(c) Choosing a card from a deck of 52 cards
(d) Thowing a stone from a roof of a building

Answer:

Throwing a stone from a roof of a building is not a random experiment.

Because, if we throw a stone from the roof of a building, we know the output it will fall on the ground.

Hence, the correct answer is option D.

Page No 42:

Question 6:

Choose the correct answer.
What is the probability of choosing a vowel from the alphabets?
(a) 2126

(b) 526

(c) 126

(d) 326

Answer:

Total number of alphabets = 26
Total number of vowels = 5 {a, e, i, o, u}

∴ Probability of choosing a vowel from the alphabets

=Total number of vowelsTotal number of alphabet=526

Hence, the correct answer is option B.

Page No 42:

Question 7:

Choose the correct answer.
In a school only, 3 out of 5 students can participate in a competition. What is the probability of the students who do not make it to the competition?
(a) 0.65
(b) 0.4
(c) 0.45
(d) 0.6

Answer:

Given: 3 out of 5 students can participate in a competition i.e. 2 out of 5 students cannot participate in the competition.
Therefore, Probability of student who do not make it to competition = 25=0.4

Hence, the correct answer is option B.

Page No 42:

Question 8:

Choose the correct answer.
Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.
Observe the pie chart given below and answer question.

Which colour received 15 of the votes?
(a) Red
(b) Blue
(c) Green
(d) Yellow

Answer:

Green (20%) i.e., 20100=15 Votes received by green.

Hence, the correct answer is option C.



Page No 43:

Question 9:

Choose the correct answer.
Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.
Observe the pie chart given below and answer question.

If 400 students voted in all, then how many did vote ‘Others’ colour as their favourite?
(a) 6
(b) 20
(c) 24
(d) 40

Answer:

Given: Total number of votes = 400
We have,
Votes for others = 6% of 400
                        =6100×400=24

Hence, the correct answer is option C.

Page No 43:

Question 10:

Choose the correct answer.
Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.
Observe the pie chart given below and answer question.

Which of the following is a reasonable conclusion for the given data?
(a) 120 th student voted for blue colour
(b) Green is the least popular colour
(c) The number of students who voted for red colour is two times the number of students who voted for yellow colour
(d) Number of students liking together yellow and green colour is approximately the same as those for red colour.

Answer:

Number of students liking together yellow and green colour is (14 + 20) = 34%, which is approximately the same as there for red colour (35%).

Hence, the correct answer is option D.

Page No 43:

Question 11:

Choose the correct  answer.
Listed below are the temperature in °C for 10 days.
–6, –8, 0, 3, 2, 0, 1, 5, 4, 4
What is the range of the data?
(a) 8
(b) 13°C
(c) 10°C
(d) 12°C

Answer:

Range of the data = maximum value – minimum value
                                         = 5 – (–8)
                                         = 13ºC
 
Hence, the correct answer is option B.

Page No 43:

Question 12:

Choose the correct  answer.
Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor is blue?
(a) 720

(b) 35

(c) 15

(d) 14

Answer:

Total number of button on the table 
                         = 4 + 7 + 3 + 6 = 20

Probability that the bottom on the floor is blue = 420=15

Hence, the correct answer is option C.

Page No 43:

Question 13:

Choose the correct  answer.
Rahul, Varun and Yash are playing a game of spinning a coloured wheel. Rahul wins if spinner lands on red. Varun wins if spinner lands on blue and Yash wins if it lands on green. Which of the following spinner should be used to make the game fair?

 
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Answer:

Spinner (iv) should be used to make the game fair as the area of each colour is equal.

Hence, the correct answer is D.



Page No 44:

Question 14:

Choose the correct  answer.
In a frequency distribution with classes 0 – 10, 10 – 20 etc., the size of the class intervals is 10. The lower limit of fourth class is
(a) 40
(b) 50
(c) 20
(d) 30

Answer:

Given: Frequency distribution with classes 0 – 10, 10 – 20 etc., and the size of the class intervals is 10.
So, the next class will be 20 – 30, 30 – 40.
Thus, the fourth class is 30 – 40.
Therefore, the lower limit of the fourth class is 30.

Hence, the correct answer is option D.

Page No 44:

Question 15:

Choose the correct  answer.
A coin is tossed 200 times and head appeared 120 times. The probability of getting a head in this experiment is
(a) 25

(b) 35

(c) 15

(d) 45

Answer:

Given: A coin is tossed 200 times and head appeared 120 times.

Then, Probability of getting a head in this experiment.

=Number of times head appearedNumber of times coin tossed=120200=35

Hence, the correct answer is option B.

Page No 44:

Question 16:

Choose the correct  answer.
Data collected in a survey shows that 40% of the buyers are interested in buying a particular brand of toothpaste. The central angle of the sector of the pie chart representing this information is
(a) 120°
(b) 150°
(c) 144°
(d) 40°

Answer:

Percentage of buyers interested in buying a particular toothpaste = 40%.

Central angle of the pie chart representing this information = 40% of central angle

=40100×360=144

Hence, the correct answer is option C.

Page No 44:

Question 17:

Choose the correct  answer.
Monthly salary of a person is Rs. 15000. The central angle of the sector representing his expenses on food and house rent on a pie chart is 60°. The amount he spends on food and house rent is
(a) Rs. 5000
(b) Rs. 2500
(c) Rs. 6000
(d) Rs. 9000

Answer:

The central angle of the sector of expenses on food and house rent on a pie chart = 60°.

Part of monthly salary he spends on food and house rent = 60360=16

Therefore, the amount he spends on food and house rent  =16×monthly salary=16×Rs. 15000=Rs. 2500

Hence, the correct answer is option B.

Page No 44:

Question 18:

Choose the correct  answer.
The following pie chart gives the distribution of constituents in the human body. The central angle of the sector showing the distribution of protein and other constituents is


(a) 108°
(b) 54°
(c) 30°
(d) 216°

Answer:

Distribution of protein and other constituents = 16 + 14 = 30%

The central angle at the sector showing the distribution of protein and other constituents =30100×360=108

Hence, the correct answer is option A.



Page No 45:

Question 19:

Choose the correct  answer.
Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?


(a) 25

(b) 15

(c) 35

(d) 45

Answer:

Total number of cards = 5
Total number of cards has the number 2 on it = 2

Therefore, Probability of Rohan picking a card without seeing, that has number 2 on it is 25.

Hence, the correct answer is option A.

Page No 45:

Question 20:

Choose the correct  answer.
The following pie chart represents the distribution of proteins in parts of a human body. What is the ratio of distribution of proteins in the muscles to that of proteins in the bones?

(a) 3 : 1
(b) 1 : 2
(c) 1 : 3
(d) 2 : 1

Answer:

Distribution of the protein in the muscles = 13
Distribution of the protein in the bones = 16
 Ratio =1316Ratio= 2 : 1

Hence, the correct answer is option D.

Page No 45:

Question 21:

Choose the correct  answer.
What is the central angle of the sector (in the above pie chart) representing skin and bones together?


(a) 36°
(b) 60°
(c) 90°
(d) 96°

Answer:

The Parts representing skin and bones together =110+16=3+530=830

Therefore, the central angle of the sector representing skin and bones together =830×360=96

Hence, the correct answer is option D.

Page No 45:

Question 22:

Choose the correct  answer.
What is the central angle of the sector (in the above pie chart) representing hormones enzymes and other proteins.


(a) 120°
(b) 144°
(c) 156°
(d) 176°

Answer:

The part representing hormones enzymes and other proteins =1-110+16+13=1-3+5+1030=1-1830=1230=25

Therefore, the central angle of the sector representing hormones enzymes and other proteins =25×360=144

Hence, the correct answer is option B.

Page No 45:

Question 23:

Choose the correct  answer.
A coin is tossed 12 times and the outcomes are observed as shown below:

The chance of occurrence of Head is
(a) 12

(b) 512

(c) 712

(d) 57

Answer:

Total number of times coin tossed = 12
Total number of times of occurrence of head = 5

Therefore, the chance of occurrence of head =Total number of heads appearedTotal number of times coin tossed=512

Hence, the correct answer is option B.

Page No 45:

Question 24:

Choose the correct  answer.
Total number of outcomes, when a ball is drawn from a bag which contains 3 red, 5 black and 4 blue balls is
(a) 8
(b) 7
(c) 9
(d) 12

Answer:

Total number of outcomes = total number of balls
                                                     = 3 + 5 + 4
                                                     = 12

Hence, the correct answer is option D.

Page No 45:

Question 25:

Choose the correct  answer.
A graph showing two sets of data simultaneously is known as
(a) Pictograph
(b) Histogram
(c) Pie chart
(d) Double bar graph

Answer:

A graph showing two sets of data simultaneously is known as "Double bar graph".

Hence, the correct answer is option D.



Page No 46:

Question 26:

Choose the correct  answer.
Size of the class 150 –175 is
(a) 150
(b) 175
(c) 25
(d) –25

Answer:

Size of the class = upper limits – lower limits
                                      = 175 – 150
                                      = 25

Hence, the correct answer is option C.

Page No 46:

Question 27:

Choose the correct  answer.
In a throw of a dice, the probability of getting the number 7 is
(a) 12

(b) 16

(c) 1

(d) 0

Answer:

In a dice, there are only 6 numbers i.e. 1, 2, 3, 4, 5 and 6.

So, there is no probability of getting the number 7.

The probability of getting the number 7 is 0.

Hence, the correct answer is option D.

Page No 46:

Question 28:

Choose the correct  answer.
Data represented using circles is known as
(a) Bar graph
(b) Histogram
(c) Pictograph
(d) Pie chart

Answer:

Data represented using circles is known as "Pie chart".

Hence, the correct answer is option D.

Page No 46:

Question 29:

Choose the correct  answer.
Tally marks are used to find
(a) Class intervals
(b) Range
(c) Frequency
(d) Upper limit

Answer:

Tally marks are used to find the frequency of the data set.

Hence, the correct answer is option C.

Page No 46:

Question 30:

Choose the correct  answer.
Upper limit of class interval 75 – 85 is
(a) 10
(b) –10
(c) 75
(d) 85

Answer:

Upper limit of class interval is the upper value of the class-interval.

So, upper limit of class interval 75 – 85 is 85.

Hence, the correct answer is option D.

Page No 46:

Question 31:

Choose the correct  answer.
Numbers 1 to 5 are written on separate slips, i.e one number on one slip and put in a box. Wahida pick a slip from the box without looking at it. What is the probability that the slip bears an odd number?
(a) 15

(b) 25

(c) 35

(d) 45

Answer:

Total number of slips = 5 (1, 2, 3, 4, 5)
Total number of odd number = 3 (1, 3, 5)

Therefore, the probability that the slips bears an odd number =Number of slips bear an odd numberTotal number of slip=35

Hence, the correct answer is option C.

Page No 46:

Question 32:

Choose the correct  answer.
A glass jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Hari takes out a marble from the jar at random. What is the probability that the chosen marble is of red colour?

(a) 710

(b) 310

(c) 45

(d) 25

Answer:

Total number of marbles = 6 + 5 + 4 + 5 = 20
Total number of marbles of red colour = 6.

Therefore, the probability that the choosen marble is of red colour =Total number of marbles of red colourTotal number of marbles=620=310

Hence, the correct answer is option B.

Page No 46:

Question 33:

Choose the correct  answer.
A coin is tossed two times. The number of possible outcomes is
(a) 1
(b) 2
(c) 3
(d) 4

Answer:

When a coin is tossed two times then, the number of possible outcome is 4 i.e. HT, TH, TT and HH.

Hence, the correct answer is option D.

Page No 46:

Question 34:

Choose the correct  answer.
A coin is tossed three times. The number of possible outcomes is
(a) 3
(b) 4
(c) 6
(d) 8

Answer:

When a coin is tossed three times, then, the number of possible outcome is 8.

HHH, HHT, HTT, TTT, HTH, THH, TTH, THT.

Hence, the correct answer is option D.

Page No 46:

Question 35:

Choose the correct  answer.
A dice is tossed two times. The number of possible outcomes is
(a) 12
(b) 24
(c) 36
(d) 30

Answer:

When a dice is tossed two times, then, the number of possible outcomes is 36.

i.e. (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Hence, the correct answer is option C.



Page No 47:

Question 36:

Fill in the blanks to make the statements true.
Data available in an unorganised form is called __________ data.

Answer:

Data available in an unorganised form is called "raw" data.

Page No 47:

Question 37:

Fill in the blanks to make the statements true.
In the class interval 20 – 30, the lower class limit is __________.

Answer:

Lower limit is the lower value of the class.
Here, the lower value of the class interval is 20.

In the class interval 20 – 30, the lower class limit is "20".

Page No 47:

Question 38:

Fill in the blanks to make the statements true.
In the class interval 26 – 33, 33 is known as __________.

Answer:

In the class interval 26 – 33, 33 is known as "upper class limit".

Page No 47:

Question 39:

Fill in the blanks to make the statements true.
The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is __________.

Answer:

Range of the data = maximum value – minimum value
                             = 25 – 6
                             = 19.

The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is "19".

Page No 47:

Question 40:

Fill in the blanks to make the statements true.
A pie chart is used to compare __________ to a whole.

Answer:

A pie chart is used to compare "a Part" to a whole.

Page No 47:

Question 41:

Fill in the blanks to make the statements true.
In the experiment of tossing a coin one time, the outcome is either __________ or __________.

Answer:

In the experiment of tossing a coin one time, the outcome is either "head" or "tail".

Page No 47:

Question 42:

Fill in the blanks to make the statements true.
When a dice is rolled, the six possible outcomes are __________.

Answer:

When a dice is rolled, the six possible outcomes are "1, 2, 3, 4, 5 and 6".

Page No 47:

Question 43:

Fill in the blanks to make the statements true.
Each outcome or a collection of outcomes in an experiment makes an __________.

Answer:

Each outcome or a collection of outcomes in an experiment makes an "event".

Page No 47:

Question 44:

Fill in the blanks to make the statements true.
An experiment whose outcomes cannot be predicted exactly in advance is called a __________ experiment.

Answer:

An experiment whose outcomes cannot be predicted exactly in advance is called a "random" experiment.

Page No 47:

Question 45:

Fill in the blanks to make the statements true.
The difference between the upper and lower limit of a class interval is called the __________ of the class interval.

Answer:

The difference between the upper and lower limit of a class interval is called the "size" of the class interval.

Page No 47:

Question 46:

Fill in the blanks to make the statements true.
The sixth class interval for a grouped data whose first two class intervals are 10 – 15 and 15 – 20 is __________.

Answer:

Given: The first two class intervals are 10 – 15 and 15 – 20.
From the above information it can be observed that the size of the class is 5.

Hence, the sixth class interval will be 35 – 40.

Page No 47:

Question 47:

Fill in the blanks to make the statements true.
The total number of people surveyed is __________.

Histogram given on the right shows the number of people owning the different number of books.

Answer:

The total number of people surveyed
                        = 8 + 14 + 5 + 6 + 2
                        = 35

Hence, the total number of people surveyed is "35".

Page No 47:

Question 48:

Fill in the blanks to make the statements true.
The number of people owning books more than 60 is __________.

Histogram given on the right shows the number of people owning the different number of books.

Answer:

The number of people owning books more than 60 = 6 + 2 = 8.

Hence, the number of people owning books more than 60 is 8.

Page No 47:

Question 49:

Fill in the blanks to make the statements true.
The number of people owning books less than 40 is __________.

Histogram given on the right shows the number of people owning the different number of books.

Answer:

The number of people owning books less than 40 = 8 + 14 = 22.

Hence, the number of people owning books less than 40 is "22".

Page No 47:

Question 50:

Fill in the blanks to make the statements true.
The number of people having books more than 20 and less than 40 is __________.

Histogram given on the right shows the number of people owning the different number of books.

Answer:

The number of people having books more than 20 and less than 40 = 14.

Hence, the number of people having book more than 20 and less than 40 is "14".

Page No 47:

Question 51:

Fill in the blanks to make the statements true.
The number of times a particular observation occurs in a given data is called its __________.

Answer:

The number of times a particular observation occurs in a given data is called its "frequency".



Page No 48:

Question 52:

Fill in the blanks to make the statements true.
When the number of observations is large, the observations are usually organised in groups of equal width called __________.

Answer:

When the number of observations is large, then to make calculation easy, the observations are usually organised in groups of equal width called class - interval.

Hence, When the total number of observations is large, the observations are usually organised in groups at equal width called "class intervals".

Page No 48:

Question 53:

Fill in the blanks to make the statements true.
The total number of outcomes when a coin is tossed is __________.

Answer:

When a coin is tossed, the possible outcomes are either heads or tails.

Hence, the total number of outcomes when a coin is tossed is 2.

Page No 48:

Question 54:

Fill in the blanks to make the statements true.
The class size of the interval 80 – 85 is __________.

Answer:

Class size of the interval = upper class limit – lower class limit
                                        = 85 – 80
                                        = 5

Hence, the class size of the interval 80 – 85 is 5.

Page No 48:

Question 55:

Fill in the blanks to make the statements true.
In a histogram __________ are drawn with width equal to a class interval without leaving any gap in between.

Answer:

In a histogram the bars are of equal length and have no gaps in between.

Hence, in a histograph, "Bars" are drawn with width equal to a class-interval without leaving any gap in between.

Page No 48:

Question 56:

Fill in the blanks to make the statements true.
When a dice is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally __________.

Answer:

When a dice is thrown, then the outcomes 1, 2, 3, 4, 5, 6 have equal chance to appear.

Hence, When a dice is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally "likely".

Page No 48:

Question 57:

Fill in the blanks to make the statements true.
In a histogram, class intervals and frequencies are taken along __________ axis and __________ axis.

Answer:

In a histogram, class intervals are taken along x-axis and frequencies are taken along y-axis.

Hence, in a histogram, class intervals and frequencies are taken along "x"-axis and "y"-axis.

Page No 48:

Question 58:

Fill in the blanks to make the statements true.
In the class intervals 10 –20, 20 –30, etc., respectively, 20 lies in the class __________.

Answer:

According to the convention the common observation will belong to the higher class.

Hence, in the class intervals 10 – 20, 20 – 30, etc., respectively, 20 lies in the class 20 – 30.

Page No 48:

Question 59:

State whether the statements are true (T) or false (F).
In a pie chart a whole circle is divided into sectors.

Answer:

True,
Pie chart is also called circle graph.


Hence, in a pie chart a whole circle is divided into sectors.

Page No 48:

Question 60:

State whether the statements are true (T) or false (F).
The central angle of a sector in a pie chart cannot be more than 180°.

Answer:

False,
The central angle of a sector in a pie chart can be more than 180° but not more than 360º.

Page No 48:

Question 61:

State whether the statements are true (T) or false (F).
Sum of all the central angles in a pie chart is 360°.

Answer:

True,
Pie chart is also called circle graph and the central angle of a circle is 360º.


Hence, sum of all the central angles in a Pie chart is 360º.

Page No 48:

Question 62:

State whether the statements are true (T) or false (F).
In a pie chart two central angles can be of 180°.

Answer:

True,


Hence, in a Pie chart two central angle can be of 180º.

Page No 48:

Question 63:

State whether the statements are true (T) or false (F).
In a pie chart two or more central angles can be equal.

Answer:

True,


Hence, in a pie chart, two or more central angles can be equal.

Page No 48:

Question 64:

State whether the statements are true (T) or false (F).
Getting a prime number on throwing a die is an event.

Answer:

True,
On throwing a dice, the outcomes are 1, 2, 3, 4, 5 and 6.
Thus, getting 2, 3 and 5 is an event.

Hence, getting a prime number on throwing a die is an event.

Page No 48:

Question 65:

State whether the statements are true (T) or false (F).
Using the following frequency table, answer question

Marks (obtained out of 10) 4 5 7 8 9 10
Frequency 5 10 8 6 12 9

9 students got full marks.

Answer:

True,
The frequency of full mark i.e., 10 is 9.

Hence, 9 students got full marks.

Page No 48:

Question 66:

State whether the statements are true (T) or false (F).
Using the following frequency table, answer question

Marks (obtained out of 10) 4 5 7 8 9 10
Frequency 5 10 8 6 12 9

The frequency of less than 8 marks is 29.

Answer:

False,
Frequency of less than 8 marks = 5 + 10 + 8 = 23

Hence, the frequency of less than 8 marks is 22.

Page No 48:

Question 67:

State whether the statements are true (T) or false (F).
Using the following frequency table, answer question

Marks (obtained out of 10) 4 5 7 8 9 10
Frequency 5 10 8 6 12 9

The frequency of more than 8 marks is 21.

Answer:

True,
Frequency of more than 8 marks = 12 + 9 = 21.

Hence, the frequency of more than 8 marks is 21.

Page No 48:

Question 68:

State whether the statements are true (T) or false (F).
Using the following frequency table, answer question

Marks (obtained out of 10) 4 5 7 8 9 10
Frequency 5 10 8 6 12 9

10 marks the highest frequency.

Answer:

False,
The highest frequency is 12; which is for 9 marks.

Hence, 9 marks has the highest frequency.

Page No 48:

Question 69:

State whether the statements are true (T) or false (F).
If the fifth class interval is 60 – 65, fourth class interval is 55 – 60, then the first class interval is 45 –50.

Answer:

False,
If the fifth class interval is 60 – 65 and fourth class interval is 55 – 60.
Thus, third class interval is 50 – 55, second class interval is 45 – 50 and first class interval is 40 – 45.

Hence, the first class interval is 40 – 45.



Page No 49:

Question 70:

State whether the statements are true (T) or false (F).
From the histogram given on the right, we can say that 1500 males above the age of 20 are literate.

Answer:

False,
Numbers of literate above the age of 20 = 600 + 800 + 500
                                                           = 1900  

Hence, We can say that 1900 males above the age of 20 are literate.

Page No 49:

Question 71:

State whether the statements are true (T) or false (F).
The class size of the class interval 60 – 68 is 8.

Answer:

True,
Class-size of the interval = upper class limit – lower class limit
                                         = 68 – 60
                                         = 8

Hence, the class size of the class interval 60 – 68 is 8.

Page No 49:

Question 72:

State whether the statements are true (T) or false (F).
If a pair of coins is tossed, then the number of outcomes are 2.

Answer:

False,
When a pair of coin tossed, the outcomes are HH, HT, TH and TT.

Hence, if a pair of coins is tossed, then the number of outcomes are 4.

Page No 49:

Question 73:

State whether the statements are true (T) or false (F).
On throwing a dice once, the probability of occurence of an even number is 12.

Answer:

On throwing a dice once, the occurrence of an even numbers can be 2, 4 and 6.
Now,
The probability of occurrence of even numbers

=Numer of even numbers on a dieTotal Numer of numbers on a die=36=12

Hence, On throwing a dice once, the probability of occurrence of an even number is 12.

Page No 49:

Question 74:

State whether the statements are true (T) or false (F).
On throwing a dice once, the probability of occurence of a composite number is 12.

Answer:

False,
On throwing a die once, the occurence of composite numbers can be 4 and 6.
Now,
The probability of occurence of a composite numbers

=Number of composite number on a dieTotal numbers on a die=26=13

Hence, On throwing a die once, the probability of occurence of a composite number is 13.

Page No 49:

Question 75:

State whether the statements are true (T) or false (F).
From the given pie chart, we can infer that production of Manganese is least in state B.

Answer:

False,

We cannot infer the least or highest in a pie chart unless the central angles are given.

Page No 49:

Question 76:

State whether the statements are true (T) or false (F).
One or more outcomes of an experiment make an event.

Answer:

True,
Each outcome at an experiment or a collection of outcomes make an event.

Hence, one or more outcomes of an experiment make an event.

Page No 49:

Question 77:

State whether the statements are true (T) or false (F).
The probability of getting number 6 in a throw of a dice is 16. Similarly the probability of getting a number 5 is 15.

Answer:

False,
The probability of getting number 6 or 5 = 16.

Hence, the probability of getting number 6 or number 5 in a throw of dice is 16.

Page No 49:

Question 78:

State whether the statements are true (T) or false (F).
The probability of getting a prime number is the same as that of a composite number in a throw of a dice.

Answer:

False,
In a throw of a dice, the occurence of prime numbers can be 2, 3, 5 and occurence of a composite number can be 4, 6.

Hence, the probability of getting a prime number is 12 and probability of getting a composite number is 13.

Page No 49:

Question 79:

State whether the statements are true (T) or false (F).
In a throw of a dice, the probability of getting an even number is the same as that of getting an odd number.

Answer:

True,
In a throw of a dice, the occurence of  even numbers can be 2, 4, 6 and occurence of odd number can be 1, 3, 5.

Hence, the probability of getting an even number or an odd number is same. i.e 12.



Page No 50:

Question 80:

State whether the statements are true (T) or false (F).
To verify pythagoras theorem is a random experiment.

Answer:

False,
The result of the Pythagoras theorem is known.

Hence, Verify Pythagoras theorem is not a random experiment.

Page No 50:

Question 81:

State whether the statements are true (T) or false (F).
The following pictorial representation of data is a histogram.

Answer:

True,
Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bar shown the frequency of the class interval, but there is no gap between the bars.

Hence, the Pictorial representation of a data is a historgram.

Page No 50:

Question 82:

Given below is a frequency distribution table. Read it and answer the questions that follow:

 
Class Interval Frequency
10 – 20 5
20 – 30 10
30 – 40 4
40 – 50 15
50 – 60 12

(a) What is the lower limit of the second class interval?
(b) What is the upper limit of the last class interval?
(c) What is the frequency of the third class?
(d) Which interval has a frequency of 10?
(e) Which interval has the lowest frequency?
(f) What is the class size?

Answer:

(a) The second class interval is 20 – 30.
     Hence, the lower limit of the second class interval is 20.

(b) The last class interval is 50 – 60.
     Hence, the upper limit of the last class is 60.

(c) The third class is 30 – 40.
     Hence, the frequency of third class i.e. 30 – 40 is 4.

(d) The frequency 10 belongs to the second class i.e 20 – 30.
      Hence, the interval 20 – 30 has a frequency of 10.

(e) The lowest frequency is 4.
      Hence, the interval 30 – 40 has the lowest frequency.

(f) Class-size  = upper class limit – lower class limit
                       = 20 – 10
                       = 10
Hence, the class size is 10.



Page No 51:

Question 83:

The top speeds of thirty different land animals have been organised into a frequency table. Draw a histogram for the given data.
 

Maximum Speed (km/h) Frequency
10 – 20 5
20 – 30 5
30 – 40 10
40 – 50 8
50 – 60 2
60 – 70 2
​

Answer:

Page No 51:

Question 84:

Given below is a pie chart showing the time spend by a group of 350 children in different games. Observe it and answer the questions that follow.



(a) How many children spend at least one hour in playing games?
(b) How many children spend more than 2 hours in playing games?
(c) How many children spend 3 or lesser hours in playing games?
(d) Which is greater — number of children who spend 2 hours or more per day or number of children who play for less than one hour?

Answer:

(a) Children spend at least one hour in playing

      =Chidren spend one hour or more than one hour in playing=Total children-children spend less then 1 hour in playing=350-6% of 350=350-6100×350=350-21=329.
      
      Hence, 329 children spend at least one hour in playing games.

(b) Children spend more than 2 hours in playing games.

      =34+4+10% of total children=48% of 350=48100×350=168
    
     Hence, 168 children spend more than 2 hours on playing games.

(c) Children spend 3 or lesser hours in playing games.

      =34+30+6+16% of total children=86% of 350=86100×350=301

      Hence, 301 children spend 3 or lesser hours in Playing games.

(d) Number of children who spend 2 hours or more per day on playing games =30+34+10+4% of total children=78% of total children

     Number of children who play for less than one hour
                                      = 6% of total children

     Hence, number of children who spend 2 hours or more per day is greater than the number of children who play for less than one hour.
 
 

Page No 51:

Question 85:

The pie chart on the right shows the result of a survey carried out to find the modes of travel used by the children to go to school. Study the pie chart and answer the questions that follow.

(a) What is the most common mode of transport?
(b) What fraction of children travel by car?
(c) If 18 children travel by car, how many children took part in the survey?
(d) How many children use taxi to travel to school?
(e) By which two modes of transport are equal number of children travelling?

Answer:

(a) The bus has the maximum central angle.
     Hence, the most common mode of transport is bus.

(b) The central angle of the car is 90º.
     Thus, the fraction of children travel by car =90º360º=14

     Hence, the fraction of children travel by car is 14.

(c) The fraction of children travel by car =14.
     Thus, the total number of children travel by car


     =14×total number of children18=14×total number of childrenTotal number of children=4×18=72.

(d) The central angle for children travel by taxi
      = 360º – (120º + 60º + 60º + 90º) = 30º
      Thus, the fraction of children travel by taxi =30º360º=112
      Therefore, number of children travel by taxi =112×72=6.

       Hence, 6 children use taxi to travel to school.

(e) The central angles of children using cycle or walk are same.
     
      Hence, the cycle and walk are two mode of transport are equal number of children travelling.



Page No 52:

Question 86:

A dice is rolled once. What is the probability that the number on top will be
(a) Odd
(b) Greater than 5
(c) A multiple of 3
(d) Less than 1
(e) A factor of 36
(f) A factor of 6

Answer:

When a dice is rolled once, the possible outcomes are 1, 2, 3, 4, 5 and 6.

(a) Probability that the number on the top will be odd =36=12.

     Hence, the probability that the number on the top will be odd is 12.

(b) The number greater than 5 is 6.

     Hence, the probability that the number on top will be greater than 5 is 16.

(c) The multiples of 3 are 3 and 6.

     Hence, the probability that the number on top will be a multiple of 3 is 26 i.e 13.

(d) There is no number on the dice which is less than 1.

      Hence, the probability that the number on top will be less than 1 is 0.

(e) The factors of 36 on a dice are 1, 2, 3, 4 and 6.
     
      Hence, the probability that the number on top will be a factor of 36 is 56.

(f) The factor of 6 on a dice are 1, 2, 3 and 6.

     Hence, the probability that the number on top will be a factor of 6 is 46 i.e. 23. 

Page No 52:

Question 87:

Classify the following statements under appropriate headings.
(a) Getting the sum of angles of a triangle as 180°.
(b) India winning a cricket match against Pakistan.
(c) Sun setting in the evening.
(d) Getting 7 when a die is thrown.
(e) Sun rising from the west.
(f) Winning a racing competition by you.

Certain to happen Impossible to happen May or may not happen
     
     

Answer:

 

Certain to happen Impossible to happen May or may not happen
(a) (d) (b)
(c) (e) (f)

(a) Certain to happen; because the sum of angles of a triangle is always 180º.

(b) May or may not happen; because result of the match is unpredictable.

(c) Certain to happen, because sum is always setting in the evening everyday.

(d) Impossible to happen; because 7 is not in a dice.

(e) Impossible to happen; because sun rising from the east.

(f) May or may not happen; because the result of a competition is unpredictable.

Page No 52:

Question 88:

Study the pie chart given below depicting the marks scored by a student in an examination out of 540. Find the marks obtained by him in each subject.

Answer:

Disclaimer: Pie chart is missing in the question.

Page No 52:

Question 89:

 Ritwik draws a ball from a bag that contains white and yellow balls. The probability of choosing a white ball is 29.  If the total number of balls in the bag is 36, find the number of yellow balls.

Answer:

Given: The probability of choosing a white ball = 29
Then, the probability of choosing a yellow ball = 1-29=79

Given, the total number of balls = 36

∴ Number of yellow ball = 79×36=28

Hence, the number of yellow ball is 28.



Page No 53:

Question 90:

Look at the histogram below and answer the questions that follow.

(a) How many students have height more than or equal to 135 cm but less than 150 cm?
(b) Which class interval has the least number of students?
(c) What is the class size?
(d) How many students have height less than 140 cm?

Answer:

(a) Number of students have height more than or equal to 135 cm but less than 150 cm = 14 + 18 + 10 = 42.

     Hence, 42 students have height more than or equal to 135 cm but less than 150 cm.

(b) The least number of students is 4, which is for the class interval 150 – 155.

     Hence, class interval 150 – 155 has the least number of students.

(c) Class size = upper class limit – lower class limit
      Let take a class 125 – 130.
      Then, size = 130 – 125 = 5

      Hence, the class size is 5.

(d) Number of students having height less than 140
      = 6 + 8 + 14 = 28

      Hence, 28 students have height less than 140 cm.

Page No 53:

Question 91:

Following are the number of members in 25 families of a village:
6, 8, 7, 7, 6, 5, 3, 2, 5, 6, 8, 7, 7, 4, 3, 6, 6, 6, 7, 5, 4, 3, 3, 2, 5.
Prepare a frequency distribution table for the data using class intervals 0 –2, 2 –4, etc.

Answer:

Class interval Frequency
0 – 2 0
2 – 4 6
4 – 6 6
6 – 8 11
8 – 10 2
Total  25
 

Page No 53:

Question 92:

Draw a histogram to represent the frequency distribution in question 91.

Answer:

Page No 53:

Question 93:

The marks obtained (out of 20) by 30 students of a class in a test are as follows:
14, 16, 15, 11, 15, 14, 13, 16, 8, 10, 7, 11, 18, 15, 14, 19, 20, 7, 10, 13, 12, 14, 15, 13, 16, 17, 14, 11, 10, 20.
Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval is 4 – 8 (excluding
8 and including 4).

Answer:


Page No 53:

Question 94:

Prepare a histogram from the frequency distribution table obtained in question 93.

Answer:




Page No 54:

Question 95:

The weights (in kg) of 30 students of a class are:
39, 38, 36, 38, 40, 42, 43, 44, 33, 33, 31, 45, 46, 38, 37, 31, 30, 39, 41, 41, 46, 36, 35, 34, 39, 43, 32, 37, 29, 26.
Prepare a frequency distribution table using one class interval as (30 – 35), 35 not included.
(i) Which class has the least frequency?
(ii) Which class has the maximum frequency?

Answer:




(i) The class 25 – 30 has the least frequency i.e. 2.

(ii) The class 35 – 40 has the maximum frequency i.e. 11.

Page No 54:

Question 96:

Shoes of the following brands are sold in Nov. 2007 at a shoe store.
Construct a pie chart for the data.

Brand Number of pair of shoes sold
A 130
B 120
C 90
D 40
E 20

Answer:

Total number of shoes sold = 130 + 120 + 90 + 40 + 20 = 400

∴ Central angles of pie chart representing the brand

(i) Brand A=130400×360º=117º(ii) Brand B=120400×360º=108º(iii) Brand C=90400×360º=81º(iv) Brand D=40400×360º=36º(v) Brand E=20400×360º=18º

The pie chart is as follows:

 

Page No 54:

Question 97:

The following pie chart depicts the expenditure of a state government under different heads.

(i) If the total spending is 10 crores, how much money was spent on roads?
(ii) How many times is the amount of money spent on education compared to the amount spent on roads?
(iii) What fraction of the total expenditure is spent on both roads and public welfare together?

Answer:

(i) Money spend on road = 10% of total spending
    =10100×10 crore=1 crore

     Hence, 1 crore was spent on roads.

(ii) Money spent on educationMoney spent on roads=25% of total spending10% of total spending

      ⇒ Money spent on education =2.5 × money spent on roads

      Hence, 2.5 times money spent on education compare to the money spent on roads.

(iii) Fraction of total expenditure spent on both roads and public welfare =10%+20%=30%=30100=310.

       Hence, 310 fraction of the total expenditure is spents on roads and public welfare. 

Page No 54:

Question 98:

The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.
 

Animals Number of animals
Deer 42
Elephant 15
Giraffe 26
Reptiles 24
Tiger 13

Answer:

Total number of animals in zoo = 42 + 15 + 26 + 24 + 13 = 120
Central angles made pie chart representing the numbers of animals.

i Deer=42120×360º=126ºii Elephant=15120×360º=45ºiii Giraffe=26120×360º=78ºiv Reptiles=24120×360º=72ºv Tiger=13120×360º=39º

The pie chart is as follows:



Page No 55:

Question 99:

Playing cards
(a) From a pack of cards the following cards are kept face down:

Suhail wins if he picks up a face card. Find the probability of Suhail winning?

(b) Now the following cards are added to the above cards:

What is the probability of Suhail winning now? Reshma wins if she picks up a 4. What is the probability of Reshma winning?
[Queen, King and Jack cards are called face cards.]

Answer:

(i) Total number of cards = 7
    Number of face card = 1 (Queen)
    ∴ Probability of picking face card = 17.

    Hence, the probability of Suhail winning is 17.

(ii) Now, Total number of card = 7 + 8 = 15
      Number of face card = 4
      ∴ Probability of Suhail winning = 415.
      Number of card 4 = 4
      ∴ Probability of Reshma winning = 415. 
     

Page No 55:

Question 100:

Construct a frequency distribution table for the following weights (in grams) of 35 mangoes, using the equal class intervals, one of them is 40 – 45 (45 not included).
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
(a) How many classes are there in the frequency distribution table?
(b) Which weight group has the highest frequency?

Answer:

Class-interval Tally marks Frequency
30 – 35 3
35 – 40 3
40 – 45 3
45 – 50 3
50 – 55 5
55 – 60 4
60 – 65 5
65 – 70 2
70 – 75     7
Total    35


(i) There are total 9 classes in the frequency distribution.

(ii) The weight group 70 – 75 has the highest frequency.



Page No 56:

Question 101:

Complete the following table:

Weights (in kg.) Tally Marks Frequency  (Number of persons)
40 – 50  
50 – 60  
60 – 70  
70 – 80  
80 – 90 |  

Find the total number of persons whose weights are given in the above table.

Answer:

Weights (in kg.) Tally Marks Frequency  (Number of persons)
40 – 50 12
50 – 60 14
60 – 70 6
70 – 80 2
80 – 90 | 1
Total   35

∴ Total number of person = 12 + 14 + 6 + 2 + 1 = 35
 

Page No 56:

Question 102:

Draw a histogram for the following data.   

Class interval 10 – 15  15 – 20 20 – 25 25 – 30 30 – 35 35 – 40
Frequency 30 98 80 58 29 50

Answer:

Page No 56:

Question 103:

In a hypothetical sample of 20 people, the amount of money (in thousands of rupees) with each was found to be as follows:
114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.
Draw a histogram of the frequency distribution, taking one of the class intervals as 50 – 100.

Answer:

Frequency distribution table:





 

Page No 56:

Question 104:

The below histogram shows the number of literate females in the age group of 10 to 40 years in a town.

(a) Write the classes assuming all the classes are of equal width.
(b) What is the classes width?
(c) In which age group are literate females the least?
(d) In which age group is the number of literate females the highest?

Answer:

(a) The histogram shows the number of literate females in the age group of 10 to 40 years in a town.

     Thus, 10 to 40 years is to be divided into class of equal width, starting with 10.

     Hence, the classes of equal width can be written as 10 – 15, 15 – 20, 20 – 25, 25 – 30, 30 – 35 and 35 – 40.

(b) The difference between the upper class limit and lower class limit is 5.
     Hence, the class width is 5.

(c) In the age group of 10 – 15, the number literate female is least.

(d) In the age group of 15 – 20, the number of literate female are highest.



Page No 57:

Question 105:

The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools:
(a) What is the class width?
(b) How many teachers are having the maximum teaching experience and how many have the least teaching experience?
(c) How many teachers have teaching experience of 10 to 20 years?

Answer:

Disclaimer: Histogram is missing in the question.

Page No 57:

Question 106:

In a district, the number of branches of different banks is given below:

Bank State Bank of India Bank of Baroda Punjab National Bank  Canara Bank
Number of Branches 30 17 15 10
Draw a pie chart for this data.

Answer:

Total number of branches = 30 + 17 + 15 + 10 = 72

∴ The central angles representing the bank are

i State Bank of Inida = 3072×360º=150ºii State Bank of Baroda = 1772×360º=85ºiii Punjab National Bank =1572×360º=75ºiv Canara Bank =1072×360º=50º

The pie chart is as follows:

Page No 57:

Question 107:

For the development of basic infrastructure in a district, a project of Rs 108 crore approved by Development Bank is as follows:
 

Item Head Road Electricity Drinking water Sewerage
Amount in crore (Rs.) 43.2 16.2 27.00 21.6

Draw a pie chart for this data.

Answer:

Central angle for each item head are:

i Road =43.2108×360º=144ºii Electricity = 16.2108×360º=54ºiii Drinking Water = 27108×360º=90ºiv Sewerage =21.6108×360º=72º

The pie chart is as follows:



 

Page No 57:

Question 108:

In the time table of a school, periods allotted per week to different teaching subjects are given below:
 

Subject Hindi English Maths Science Social Science Computer Sanskrit
Periods Allotted 7 8 8 8 7 4 3

Draw a pie chart for this data.

Answer:

Total periods = 7 + 8 + 8 + 8 + 7 + 4 + 3 = 45

Subject Periods Central angle
Hindi 7 745×360º=56º
English 8 845×360º=64º
Maths 8 845×360º=64º
Science 8 845×360º=64º
Social Science 7 745×360º=56º
Computer 4 445×360º=32º
Sanskrit 3 345×360º=24º

 

Page No 57:

Question 109:

A survey was carried out to find the favourite beverage preferred by a certain group of young people. The following pie chart shows the findings of this survey.
From this pie chart answer the following:

(i) Which type of beverage is liked by the maximum number of people.
(ii) If 45 people like tea, how many people were surveyed?

Answer:

(i) The percentage of people preffered cold drinks is maximum.
     
     Hence, cold drinks is liked by the maximum number of people.

(ii) The number of people like tea = 45

     15% of total people surveyed=4515100×total people surveyed=45Total people surveyed=45×10015=300

      Hence, 300 people are surveyed.



Page No 58:

Question 110:

The following data represents the approximate percentage of water in various oceans. Prepare a pie chart for the given data.
 

Pacific 40%
Atlantic 30%
Indian 20%
Others 10%

Answer:

Ocean Central angle
Pacific 40100×360º=144º
Atlantic 30100×360º=108º
Indian 20100×360º=72º
Others 10100×360º=36º


The pie chart is as follows:

Page No 58:

Question 111:

At a Birthday Party, the children spin a wheel to get a gift. Find the probability of

(a) getting a ball
(b) getting a toy car
(c) any toy except a chocolate

Answer:

Total number of events = 8

The probability of
(a)  getting a ball =Number of events of getting a ballTotal number of events=28=14

     Hence, the probability of getting a ball is 14.

(b) getting a toy car =Number of events of getting a carTotal number of events=38

     Hence, the probability of getting a car =38.

(c) any toy except a chocolate =Number of events of getting any gift except a chocolateTotal number of events=78
     Hence, the probability of getting any toy except a chocolate is 78.
 

Page No 58:

Question 112:

Sonia picks up a card from the given cards.

Calculate the probability of getting
(a) an odd number
(b) a Y card
(c) a G card
(d) B card bearing number > 7

Answer:

Total number of cards = 10

(a) Number of cards having odd number = 5
     
      Hence, the probability of getting an odd number =510=12

(b) Number of Y - card = 3
 
      Hence, the probability of getting a Y - card =310.

(c) Number of G card = 2

     Hence, the probability of getting a G card =210=15.

(d) Number of B card bearing number > 7 = 0

     Hence, the probability of getting B card bearing number > 7 =010=0.

 

Page No 58:

Question 113:

Identify which symbol should appear in each sector.

Answer:

Total quantity of four symbols = 800 + 700 + 550 + 450 = 2500

From the pie chart:

i 28% of 2500 =28100×2500=700ii 32% of 2500 =32100×2500=800iii 22% of 2500 =22100×2500=550iv 18% of 2500=18100×2500=450

Hence, 
 



Page No 59:

Question 114:

Identify which symbol should appear in each sector.

Answer:

Total quantity of symbol = 192 + 228 + 180 = 660

From pie chart

i 38% of 600=38100×600=228ii 32% of 600=32100×600=192iii 30% of 600=30100×600=180Hence, 38% Yellow colour              32% Red colour              30%Pink colour


 

Page No 59:

Question 115:

A financial counselor gave a client this pie chart describing how to budget his income. If the client brings home Rs. 50,000 each month, how much should he spend in each category?

Answer:

No. Category Money spent
1. Housing 30100×50000=15,000
2. Food (including eating out) 20100×50000=10,000
3. Car loan & maintenance 25100×50000=12,500
4. Utilities 10100×50000=5,000
5. Phone 5100×50000=2,500
6. Clothing 5100×50000=2,500
7. Entertainment 5100×50000=2,500

Page No 59:

Question 116:

Following is a pie chart showing the amount spent in rupees (in thousands) by a company on various modes of advertising for a product.

Now answer the following questions.
1. Which type of media advertising is the greatest amount of the total?
2. Which type of media advertising is the least amount of the total?
3. What percent of the total advertising amount is spent on direct mail campaigns?
4. What percent of the advertising amount is spent on newspaper and magazine advertisements?
5. What media types do you think are included in miscellaneous? Why aren’t those media types given their own category?

Answer:

1. The sector having highest portion is of newspaper.

    Hence, the greatest amount of the total is spent in the advertisement of newspaper.

2. The sector having least portion is of radio.

    Hence, the least amount of the total is spent in the advertisement of Radio.

3. Total amount spent = 40 + 42 + 23 + 7 + 11 + 39 + 14 + 15 + 9
                                   = 200

    Then, 
    The total advertisement amount spent on direct main campaigns =39200×100=19.5%

     Hence, 19.5% of the total advertising amount is spent on direct main campaigns.

4. The total advertising amount is spent on newspaper and magzine =42+23200×100=32.5%

     Hence, 32.5% the total advertising amount is spent on newspaper and magzine advertisements.

5. Internet, web media, social media are included in miscellaneous.



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