# Data Handling Class-8 ML Aggarwal ICSE Maths

Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19. We provide step by step Solutions of Exercise / lesson-19 Data Handling Class-8th ML Aggarwal ICSE Mathematics.

Our Solutions contain all type Questions with Exe-19.1 , Exe-19.2 , Exe-19.3,  Objective Type Questions (including Mental Maths Multiple Choice Questions, Value Based Questions , HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.

## Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

— : Select Topics : —

Exe-19.1,

Exe-19.2 ,

Exe-19.3,

Objective Type Questions,

Mental Maths,

Multiple Choice Questions ,(MCQ)

Value Based Questions

HOTS

### Ex 19.1,Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions

Question 1.
The result of a survey of 200 people about their favourite fruit is given below:

Represent the above data by a bar graph.

The bar graph is given below:

Question 2.
Mr Khurana has two kitchen appliance stores. He compares the sales of two stores during a month and recovered as given below:

Represent the above data by a double bar graph.

The double graph of the above given data is given below:

Question 3.
The number of goals scored by a football team in different matches is given below:
3, 1, 0, 4, 6, 0, 0, 1, 1, 2, 2, 3, 5, 1, 2, 0, 1, 0, 2, 3, 9, 2, 0, 1, 0, 1, 4, 1, 0, 2, 5, 1, 2, 2, 3, 1, 0, 0, 0, 1, 1, 0, 2, 3, 0, 1, 5, 2, 0
Make a frequency distribution table using tally marks.

Frequency table is given below:

Question 4.
Given below a bar graph:

(i) What is the information given by the bar graph?
(ii) On which item the expenditure is maximum?
(iii) On which item the expenditure is minimum?
(iv) State whether true or false:
Expenditure on education is twice the expenditure on clothing.

(i) In the given bar graph, representation of the expenditure
of monthly salary on different heads is given.
(ii) On food, expenditure is maximum.
(iii) On clothing expenditure is minimum,
(iv) Yes, it is true.

Question 5.
Given below a double bar graph.

(i) What is the information given by the double graph?
(ii) Which mode of transport girls using more than the boys?
(iii) Which mode of transport boys using the most?
(iv) In which mode of transport number of girls is half the number of boys?

From the double bar graph:
(i) It represent the number of boys and girls using
different modes of transport for going to school.
(ii) In school bus, girls use more than the boys.
(iii) Boy are using the bicycle most.
(iv) In walking, number of girls is half of the number of boys

Question 6.
Using class intervals 0-5, 5-10, construct the frequency distribution table for the following
data:
13, 6, 12, 9, 11, 14, 2, 8, 18, 16, 9, 13, 17, 11, 19, 6, 7, 12, 22, 21, 18, 1, 8, 12, 18.

The required frequency table is given below:

Question 7.
Given below are the marks secured by 35 students in a surprise test:
41, 32, 35, 21, 11, 47, 42, 00, 05, 18, 25, 24, 29, 38, 30, 04, 14, 24, 34, 44, 48, 33, 36, 38, 41, 48, 08, 34, 39, 11, 13, 27, 26, 43, 03.
Taking class invervals 0-10, 10-20, …….. construct frequency distribution table. Find the number
of students obtaining below 20 marks.

Below is given the frequency table of the given data:

Number of students getting below 20 marks are = 5 + 5 = 10

Question 8.
The electricity bills (in ?) of 40 houses in a locality are given below:
78, 87,81,52, 59, 65, 101, 108, 115, 95, 98, 65,62, 121, 128, 63,76, 84, 89,91,65, 101,95,81, 87, 105, 129, 92, 75, 105, 78, 72, 107, 116, 127, 100, 80, 82, 61, 118 Construct a grouped frequency distribution table of class size 10.
Class intervals (Electricity bill in ?) Tally marks Frequency (Number of houses)

Question 9.
Draw a histrogram for the frequency table made for data in Question 8, and answer the following questions:
(i) Which group has the maximum number of houses?
(ii) How many houses pay less than ₹ 100?
(iii) How many houses pay ₹ 100 or more?

Histogram of the given data in Question 8, is given below (next page):

(i) Maximum number of house are in the group 80-90.
(ii) Number of houses who play less then ₹100 = 2 + 6 + 5 + 8 + 5 = 26
(iii) Number of houses who pay ₹ 100 or more = 7 + 3 + 4= 14

Question 10.
The weights of 29 patients in a hospital were recorded as follows:

Draw a histogram to represent this data visually.

The histogram of the above-given data is given below:

Question 11.
In a study of diabetic patients, the following data was obtained:

Represent the above data by a histogram.

The histogram representing the above-given data is given below:

Question 12.
The histogram showing the weekly wages (in ₹) of workers in a factory is given alongside:

(i) What is the frequency of class 400-425?
(ii) What is the class having a minimum frequency?
(iii) How many workers get more than ₹425?
(iv) How many workers get less than ₹475?
(v) Number of workers whose weekly wages are more than or equal to ₹400 but less than ₹450.

In the given histogram showing the weekly wages of workers in a factory.
(i) Frequency of class 400-425 is 18.
(ii) Class 475-500 has the minimum frequency.
(iii) Number of workers getting more then ₹425 is 34.
(iv) Number of workers getting less than ₹475 is 54.
(v) Number of workers whose weekly wages is more than
or equal to ₹400 but less than ₹450 = 28.

Question 13.
The number of hours for which students of a particular class watched television during holidays is shown in the histogram below.

(i) For how many hours did the maximum number of students watch T.V.?
(ii) How many students watched T.V. for less than 4 hours?
(iii) How many students spent more than 5 hours in watching T.V.?
(iv) How many students spent more than 2 hours but less than 4 hours in watching T.V.?

From the histogram given,
(i) Maximum number of students who watch 4-5 hours.
(ii) Number of students who watch T.V. for less than 4 hours is 34.
(iii) Number of students who spent more than 5 hours in watching the T.V. is 14.
(iv) Number of students who spent more than 2 hours
but less than 4 hours watching T.V. is 30.

Question 14.
The number of literate females in the age group of 10 to 40 years in a town is shown in the histogram alongside.

(i) Write the classes assuming all the classes are of equal width.
(ii) What is the class size?
(iii) In which age group are the literate females the least?
(iv) In which age group is the number of literate females the highest?

(i) The classes having an equal width are
10-15, 15-20, 20-25, 25-30, 30-35, 35-40.
(ii) The class size is 5.
(iii) The literate females are least in the age group of 10-15.
(iv) The literate females are highest in the age group of 15-20.

### Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Ex 19.2

Question 1.
The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.

Pie chart for the data is given below:

Question 2.
The following data represents the monthly expenditure of a family (in T) on various items. Draw a pie chart to represent this data.

Pie chart representing the above given data is given:

Question 3.
The following data represents the percentage distribution of the expenditure incurred in publishing a book.

Draw a pie chart to represent this data.

Pie chart representing the above given data is given:

Question 4.
The following data represents the number of students got admission in different streams of a college:

Draw a pie chart to represent this data.

Pie chart representing the above given data is given below:

Question 5.
The adjoining pie chart shows the expenditure of a country on various sports during year 2012. Study the pie chart carefully and answer the following questions:

(i) What percent of total expenditure is spent on cricket?
(ii) How much percent more is spent on hockey than that on tennis?
(iii) If the total amount spent on sports in 2012 is ₹1,80,00,000, then find amount spent on Badminton,
(iv) If the total amount spent on sports in 2012 is ₹2,40,00,000 then find the amount spent on cricket and hockey together.

From the given pie chart representing the expenditure
incurred on various sports during 2012.
(i) Expenditure on cricket = 90° = $\frac{90}{360^{\circ}}$ × 100% = 25%
(ii) Expenditure on hockey = 75° = $\frac{75}{360^{\circ}} \times 100 \%=\frac{125}{6} \%=20 \frac{5}{6} \%$
∴ $\frac{125}{6}-\frac{125}{9}=\frac{125}{18}=6.95 \%$ more
Expenditure on tennis = 50° = $\frac{50}{360^{\circ}}$ × 100% = $\frac{125}{9} \%$% = 13.9%
(iii) Total amount spent on sports = ₹1,80,00,000
Then amount spent on Badminton = ₹ 1,80,00,000 × $\frac{60}{360^{\circ}}$ = ₹30,00,000
(iv) If total amount spent on sports = 2,40,00,000,
then amount spent on cricket and hockey together
= 90° + 75° = 165° = $\frac{165^{\circ}}{360^{\circ}}$ × 2,40,00,000 = 1,10,00,000

Question 6.
The adjoining pie chart shows the number of students enrolled in class VI to class X of a school.

If 1440 students are enrolled from VI to X, then answer the following questions:
(i) How many students are enrolled in class VIII?
(ii) How many students are more in class IX than in class X?
(iii) What is the sum of students enrolled in VII and VIII?
(iv) Find the ratio of students enrolled in VI to students enrolled in X.

The given pie chart is representing the enrolment of
students from class VI to class X in a school.
Total students were enrolled = 1440
(i) Enrolment of class VIII = $\frac{85}{360^{\circ}}$ × 1440 = 340 students
(ii) Difference in X and IX class enrolement = 75° – 50 = 250°
$\frac{25}{360^{\circ}}$ × 1440 = 100 students
(iii) Sum of students enrolled in VII and VIII classes
= 70° + 85° = 155° = $\frac{155}{360^{\circ}}$ × 1440 = 620 students
Ratio between the students enrolled in VI to
students enrolled in X classes = 80° : 50° = 8 : 5

### ML Aggarwal Solutions Data Handling Exe-19.3 Class-8 ICSE Mathematics

Question 1.

List the outcomes you can see in these experiments.

(i) Outcomes in spinning wheel = A, A, A, B, C, D.
(ii) Outcomes in drawing a ball from a bag containing 5 identical balls
of different colours, says Red, black, green, blue, yellow.

Question 2.
A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3

Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
(i) Even numbers : 2, 4, 6
i.e. Favourable outcomes = 3
∴ Probability P(E) = $\frac{3}{6}=\frac{1}{2}$
(ii) Multiple of 3 = 3, 6
i.e. Favourable outcomes = 2
∴ Probability P(E) = $\frac{2}{6}=\frac{1}{3}$
(iii) Not a multiple of 3 = 1, 2, 4, 5
i.e., favourable outcomes = 4
∴ Probability P(E) = $\frac{4}{6}=\frac{2}{3}$

Question 3.
Two coins are tossed together. Find the probability of getting
(i) two tails
(ii) at least one tail
(iii) no tail

When two coins are tossed together, then
Total outcomes = 2 × 2 = 4
i.e. HH, HT, TH, TT
(i) Favourable outcomes of getting two tails = 1
∴ Probability P(E) = $\frac{1}{4}$
(ii) Favourable outcomes of getting at least one tail
TH, HT, TT = 3
∴ Probability P(E) = $\frac{3}{4}$
(iii) Favourable outcomes of getting No tail: HH = 1
∴ Probability P(E) = $\frac{1}{4}$

Question 4.
Three coins are tossed together. Find the probability of getting
(ii) at least one tail
(iii) at most one tail.

Three coins are tossed together.
∴ Total outcomes = 8
= HHH, HHT, HTH, THH, HTT, TTH, TTT, THT
(i) Favourable outcomes of getting
At least two heads : These can be HHH, HHT, HTH, THH = 4 in numbers
∴ P(E) = $\frac{\text { Number of favourable outcome }}{\text { Number of all possible outcome }}=\frac{4}{8}=\frac{1}{2}$
(ii) Favourable outcomes of getting
At least one tail: There can be HHT, HTH, HTT, TTT, THH, THT, TTH = 7 in number
∴ P(E) = $\frac{\text { Number of favourable outcome }}{\text { Number of all possible outcome }}=\frac{7}{8}$
(iii) Favourable outcomes of getting
At most one tail: There can be HHH, HHT, HTH, THH = 4
∴ P(E) = $\frac{\text { Number of favourable outcome }}{\text { Number of all possible outcome }}=\frac{4}{8}=\frac{1}{2}$

Question 5.
Two dice are rolled simultaneously. Find the probability of getting
(i) the sum as 7
(ii) the sum as 3 or 4
(iii) prime numbers on both the dice.

Two dice are rolled simultaneously
Total outcomes = 6 × 6 = 36
(i) Sum as 7 : (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
∴ Probability P(E) = $\frac{\text { Favourable oucomes }}{\text { Total outcomes }}=\frac{6}{36}=\frac{1}{6}$
(ii) The sum as 3 or 4
(1, 2), (1, 3), (2, 1), (2, 2), (3, 1) = 5
∴ Probability P(E) = $\frac{\text { Favourable oucomes }}{\text { Total outcomes }}=\frac{5}{36}$
(iii) Prime numbers on both the dice
(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5) = 9
∴ Probability P(E) = $\frac{\text { Favourable oucomes }}{\text { Total outcomes }}=\frac{9}{36}=\frac{1}{4}$

Question 6.
A fcox contains 600 screws, one tenth are rusted. One screw is taken out at random from the box. Find the probability that it is
(i) a rusted screw
(ii) not a rusted screw

Rusted screw = $\frac{1}{10}$ of 60° = $\frac{1}{10}$ × 600 = 60 seconds
(i) Favourable outcomes of picking rusted screw = 60
P(E) = $\frac{60}{600}=\frac{1}{10}$
(ii) P (of not a rusted screw) = 1 – P (rusted screw) = 1 – $\frac{1}{10}=\frac{9}{10}$

Question 7.
A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel?

‘TRIANGLE’
Total number of outcomes = 8
Vowels : I, A, E = 3
∴ Probability P(E) = $\frac{3}{8}$

Question 8.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag, find the probability the ball is drawn is
(i) white
(ii) not black
(iii) red or black
(iv) neither red nor black

In a bag, there are 5 red, 6 black and 4 white balls.
Total number of outcomes = 5 + 6 + 4=15
(i) Probability of white ball = $\frac{4}{15}$
(ii) Probability of not black (5 + 4 = 9) balls = $\frac{9}{15}=\frac{3}{5}$
(iii) Probability of red or black ball (5 + 6 = 11)= $\frac{11}{15}$
(iv) Probability of ball which is neither red nor black, white ball (4) P(E) = $\frac{4}{15}$

Question 9.
A box contains 17 cards numbered 1, 2, 3, ……….,17 and are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) odd
(ii) even
(iii) prime
(iv) divisible by 3
(v) divisible by 2 and 3 both

A box contains 17 cards numbered 1 to 17
Total number of outcomes = 17
(i) Card bearing odd number (1, 3, 5, 7, 9, 11, 13, 15, 17) = 9
∴Probability P(E) = $\frac{9}{17}$
(ii) Even number (2, 4, 6, 8, 10, 12, 14, 16) = 8
∴Probability P(E) = $\frac{8}{17}$
(iii) Prime numbers {2, 3, 5, 7, 11, 13, 17) = 7
∴Probability P(E) = $\frac{7}{17}$
(iv) Numbers divisible by 3 = 3, 6, 9, 12, 15 = 5
∴Probability P(E) = $\frac{5}{17}$
(v) Number divisible by 2 and 3 both 6, 12 = 2
∴Probability P(E) = $\frac{2}{17}$

Question 10.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is:
(i) an ace
(ii) a red card
(iii) neither a king nor a queen
(iv) a red face card or an ace
(vi) non-face card of red colour.

Number of playing cards in a deck = 52
One card is drawn
(i) An ace : 4
∴ Probability P(E) = $\frac{4}{52}=\frac{1}{13}$
(ii) A red card = 13 + 13 = 26
∴ Probability P(E) = $\frac{26}{52}=\frac{1}{2}$
(iii) Neither a king nor a queen
Number of cards 52 – (4 + 4) = 52 – 8 = 44
∴ Probability P(E) = $\frac{44}{52}=\frac{11}{13}$
(iv) A red face card = 6
∴ Probability P(E) = $\frac{6}{52}=\frac{3}{26}$
(v) A card of spade or an ace = 13 + 3 = 16
∴ Probability P(E) = $\frac{16}{52}=\frac{4}{13}$
(vi) Non-face card of red colour = 26 – 6 = 20
∴ Probability P(E) = $\frac{20}{52}=\frac{5}{13}$

Question 11.
In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.

Number of prized tickets = 5
Number of blank tickets = 995
Total number of tickets = 5 + 995 = 1000
Probability of prized ticket
$P(E)=\frac{\text { Number of favourable outcome }}{\text { Number of possible outcome }}$
$\frac{5}{1000}=\frac{1}{200}$

### Objective Type Questions, Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

#### Mental Maths

Question 1.
Fill in the blanks:
(i) Bar graphs are ……….. representation of ungrouped data.
(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called ………..
(iii) The mid point of the class interval is called ………..
(iv) Bar graphs of grouped data are called ………..
(v) The circle graphs are commonly called ………..
(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called ………..
(vii) The outcomes which ensures the occurrence of an event are called ………..
(viii) An event which never happens is called ………..

(i) Bar graphs are visual representation of ungrouped data.
(ii) In a grouped frequency distribution, the difference between lower limit
and upper limit of a class is called class size or class width.
(iii) The mid point of the class interval is called class mark.
(iv) Bar graphs of grouped data are called histogram.
(v) The circle graphs are commonly called pie chart or pie diagram.
(vi) An experiment which has more than one possible outcomes
and it is not possible to predict the outcome in advance
is called random experiment.
(vii) The outcomes which ensures the occurrence of
an event are called favourable outcomes.
(viii) An event which never happens is called impossible event.

#### Question 2.

State whether the following statements are true (T) or false (F):
(i) The data arranged in ascending or descending order of size is called data array.
(ii) The lower limit of class 10-20 is 20.
(iii) The class size of class 20-30 is 10.
(iv) The class mark of 25-35 is 30.
(v) There is no difference between bar graphs and histograms.
(vi) In histograms the breadth of a rectangle is meaningless.
(vii) In histograms, there is no gap between two adjacent rectangle.
(viii) In a pie chart, size of each sector is proportional to the value of item represented by it.
(ix) In a pie chaiangle of sector
$\frac{\text { value of item }}{\text { sum of values of all items }} \times 180^{\circ}$
(x) In tossing a coin getting head or tail are equally likely events.
(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1.
(xii) P(occurrence of an event) = P(non occurence of an event).
(xiii) Total number of outcomes when two dice are rolled togehter = 6 + 6.

(i) The data arranged in ascending or descending
order of size is called data array. True
(ii) The lower limit of class 10-20 is 20. False
Correct: Lower limit is 10.
(iii) The class size of class 20-30 is 10. True
(iv) The class mark of 25-35 is 30. True
(v) There is no difference between bar graphs and histograms. False
Correct:
Histogram is for continued classed and in
bar graph there is gap between the two bars.
(vi) In histograms the breadth of a rectang is meaningless. False
Correct:
The rectangles are of equal width.
(vii) In histograms, there is no gap between two adjacent rectangle. True
(viii) In a pie chart, size of each sector is proportional
to the value of item represented by it. True
(ix) In a pie chart, angle of sector =
$\frac{\text { value of item }}{\text { sum of values of all items }} \times 180^{\circ}$ False
Correct:
It is $\frac{\text { value of item }}{\text { sum of values of all items }}$ × 360°
(x) In tossing a coin getting head or tail are equally likely events. True
(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1. True
(xii) P(occurrence of an event) = P(non-occurence of an event). False
Correct:
Probability is of occurence of an event.
(xiii) Total number of outcomes when two dice are rolled together = 6 + 6. False
Correct: It is 6 × 6 = 36

### Multiple Choice Questions

MCQs, Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

Study the following frequency distribution table:

The table shows the pocket money (in ?) per month of 50 students. Choose the correct answer from the given four options for questions 3 to 7;

 Class interval (Pocket money in T) Frequency (No. of students) 10-20 14 20-30 11 30-40 11 40-50 10 50-60 4 Total 50

Question 3.
Size of the class-intervals is
(a) 50
(b) 20
(c) 10
(d) 30

Size of the class interval is 10. (c)

Question 4.
The class having the maximum frequency is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 40-50

The class having the maximum frequency is 10-20. (a)

Question 5.
The upper limit of the class having minimum frequency is
(a) 30
(b) 40
(c) 50
(d) 60

The upper limit of the class having minimum frequency is 60. (d)

Question 6.
Which two are classes having the same frequency?
(a) 10-20 and 20-30
(b) 20-30 and 30-40
(c) 30-40 and 50-60
(d) 40-50 and 50-60

The two-class 20-30 and 30-40 have the same frequency. (b)

Question 7.
The frequency of class whose class mark is 25 is
(a) 14
(b) 11
(c) 10
(d) 4

25 is the class mark of the class whose frequency is 11. (b)

The pie graph shown in the adjoining figure representing the different subjects liked by the students of class VIII. Study the pie graph carefully and choose the correct answer from the given four options for questions 8 to 11.

Question 8.
Which subject is liked by the maximum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English

Mathematics is liked by the maximum number of students. (a)

Question 9.
Which subject is liked by the minimum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English

English is liked by the minimum number of students. (d)

Question 10.
If there are 200 students in class VIII then the number of students who like S. Science
(a) 10
(b) 20
(c) 40
(d) 80

In class VIII, there are 200 students,
then the number of students who like S. Science
= 200 × $\frac{20}{100}$ = 40 (c)

Question 11.
Number of students who like Science
(a) 20
(b) 40
(c) 60
(d) 80

Number of students who like science = 200 × $\frac{30}{100}$ = 60 (c)

Choose the correct answer from the given four options (12 to 17):
Question 12.
Probability of getting the sum as 4 when a pair of dice is rolled

A pair of dice is rolled, then total number of outcomes = 6 × 6 = 36
Getting sum as 4 (1, 3), (2, 2), (3, 1) = 3
Probability P(E) = $\frac{3}{36}=\frac{1}{12}$ (b)

Question 13.
Probability of getting exactly 2 heads when three coins are tossed together

Three coins are tossed,
then total number of outcomes = 23 = 2 × 2 × 2 = 8
Getting two heads (2, 2…), (2…, 2), (…2, 2) = 3
Probability = $\frac{3}{8}$ (c)

Question 14.
Probability of selecting a consonant from the letters of the word ‘FATHER’

From the letter ‘FATHER’
Total outcomes = 6
∴ Consonant = $\frac{4}{6}=\frac{2}{3}$ (d)

Question 15.
Probability of getting more than 2 heads when a pair of coins is tossed.
(a) 1
(b) $\frac{1}{2}$
(c) $\frac{1}{3}$
(d) 0

A pair of coins tossed, then
Total number of outcomes = 2 × 2 = 4
Getting more than two heads – None
∴ Probability = 0 (d)

Question 16.
Probability of getting a red ball from a bag containing 20 red balls
(a) 0
(b) 1
(c) $\frac{1}{20}$
(d) $\frac{1}{2}$

Total red balls = 20
Probability a red ball = $\frac{20}{20}$ = 1 (b)

Question 17.
Probability of getting a non-red ball from a bag containing 4 red, 5 blue and 3 black balls is

In a bag, there are 4 red balls, 5 blue and 3 black balls.
∴ Total outcomes = 4 + 5 + 3 = 12
Probability of a non-red ball (5 blue + 3 black) = 8
$\frac{8}{12}=\frac{2}{3}$ (b)

### Value Based Questions

Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

Question 1.

Draw a pie chart of the data given below:
The time spent by a Class VIII student during a day.

Should a student of class VIII study for just 2 hours daily? Which time is considered the best time for self-study?

Time spent during a day

Pie chart of the above data is given here:

More time should be given for self-study and it should be
early in the morning when the mind is fresh.

Question 2.
From a bag containing 2 saffron, 3 white and 4 green balls a ball is drawn at random. Find the probability that ball drawn is
(i) Saffron
(ii) White
(iii) Green
Which are three colours in our National Flag? What values did they indicate? What values are being promoted?

A bag contains 2 saffron, 3 white and 4 green ball
∴ Total outcomes = 2 + 3 + 4 = 9
One ball is drawn at random.
(i) Probability of a saffron ball P(E) = $\frac{2}{9}$
(ii) Probability of a white ball P(E) = $\frac{3}{9}=\frac{1}{3}$
(iii) Probability of a green ball P(E) = $\frac{4}{9}$
These three colours are of our national flag.
Saffron colour is for braving and sacrifice,
white is for peace and green is for the prosperity of the nation.

Question 3.
Four defective oranges are accidentally mixed with 16 good ones. One orange is drawn at random. Find the probability that the orange drawn is good one.
What will happen if 4 bad persons are mixed with 16 good ones?

Four defective oranges are mixed with 16 good oranges.
∴ Total number of outcomes = 4 + 16 = 20
One orange is drawn at random.
∴ Probability of an orange being a good one = $\frac{16}{20}=\frac{4}{5}$
Similarly, when 4 bad boys are mixed with 16 good boys,
they will spoil the good boys.
Bad boys arc curse on society. So, try to avoid them.

### Higher Order Thinking Skills

HOTS, Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

Question 1.

A bag contains 12 balls out of which x are black.
(i) If a ball drawn at random, what is the probability that it will be a black ball?
(ii) If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i). Find the value of x.

In a bag there are 12 balls, x is black.
(i) A bal1 is drawn at random.
Probability of a ball being black P(E) = $\frac{x}{12}$
(ii) By putting 6 more black balls, total number of black balls = x + 6
and total balls = 12 + 6 = 18
Now, probability of a black ball = $\frac{x+6}{18}$
According to the condition,
$\frac{x+6}{18}=2 \times \frac{x}{12}$
6x + 36 = 18 ⇒ 36 = 18x – 6x = 12x
∴ x = $\frac{36}{12}$ = 3

Question 2.

Ankita and Nagma are friends. They were both born in 1998. What is the probability that they have
(i) same birthday?
(ii) different birthday?

Ankita and Nagma both born in 1998.
(i) Probability of being same birth date = $\frac{1}{365}$.
(ii) Probability of being different birth dates = $\frac{365-1}{365}=\frac{364}{365}$.

Data Handling Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-19

Question 1.
Each student from the group of 40 students was asked to roll a dice independently. The results are given below:
2, 3, 3, 4, 1, 5, 2, 6, 1, 4, 2, 3, 4, 4, 6, 1, 5, 5, 2, 4, 5, 5, 3, 1, 6, 5, 4, 2, 3, 6, 1, 1, 4, 4, 5, 3, 2, 2, 6,6
Make a frequency distribution table for the same.

Frequency table of the given data is given below:

Question 2.
The marks obtained by 30 students of a class in a test of maximum marks 20 are as follows:
15, 11, 12, 10, 9, 8, 19, 13, 16, 3, 2, 17, 18, 19, 14, 6, 20, 15, 16, 12, 10, 4, 9, 8, 12, 17, 18, 20, 19, 12.
Prepare a frequency distribution table for the above data using class intervals 0-4, 4-8 and so on.

Frequency distribution table is given below:

Question 3.
Construct a frequency distribution table for the following weights (in grams) of 35 oranges, using class intervals 40—45, 45-50 and so on.
30, 40, 45, 32, 43, 50, 55, 63, 72, 73, 62, 61, 54, 53, 50, 43, 76, 38, 54, 55, 66, 70, 74, 75, 45, 47, 59, 58, 60, 63, 74, 33, 35, 70, 68.
(i) How many classes are there in the frequency distribution table?
(ii) Which weight group has the lowest frequency?
(iii) Which weight group has the highest frequency?

Frequency distribution table is given below:

(i) Number of classes =10.
(ii) Group (class) 35-40, 65-70 and 75-80 have lowest frequency,
(iii) Class 70-75 has the highest frequency.

Question 4.
Draw a histrogram of the following data:
Marks obtained by students in a Mathematics Paper of maximum marks 100.

The histogram regarding the given data is given here:

Question 5.
The following data represents the number of students using different mode of transportation to come to school.

 Mode of transport Bicycle School bus Car Walking Number of students 360 240 80 120

Draw a pie chart to represent this data.Pie chart is given below:

Pie chart is given below:

Question 6.
Answer the following questions based on the pie chart given below:
(i) Which type of programmes are viewed the most?
(ii) Which type of programmes are viewed the least?
(iii) Which two types of programmes have number of viewers equal to those watching sports channels?

From the given pie chart,
(i) Entertainment is viewed the most.
(ii) Informative is viewed the least.
(iii) Viewers of sports is equal to the
sum of the viewers of news and informative.

Question 7.
Suppose you spin the wheel shown in adjoining figure.
(i) List the outcomes of getting a green sector and not getting a green sector on this wheel.
(ii) Find the probability of getting a green sector.
(iii) Find the probability of not getting a green sector.

In the spin wheel, 3 sectors are red and 5 sectors are green.
(i) Getting green sector are G, G, G, G, G
and not getting a green sector is R, R, R.
Total number of outcomes = 5 + 3 = 8
(ii) Probability of getting a green sector P(E) = $\frac{5}{8}$.
(iii) Probaility of getting a non-green sector P(E) = $\frac{3}{8}$

Question 8.
A bag has 4 red and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is the probability of getting
(i) a red ball?
(ii) not a red ball?

In a bag, there are 4 red, 2 yellow balls.
∴ Total number of balls = 4 + 2 = 6
(i) One ball is drawn at random.
Probability of getting a red ball = $\frac{4}{6}=\frac{2}{3}$.
(ii) Probability of getting not a red ball = $\frac{2}{6}=\frac{1}{3}$.

Question 9.
Three coins are tossed together, find the probability of getting

Three coins are tossed together.
∴ Number of total outcomes = (2)3 = 2 × 2 × 2 = 8
(i) Probability of getting at the most 2 heads P(E)
= HTT, HHT, HTH, HTT, THH, TTH, THT = 7
$\frac{7}{8}$
(ii) Probability of getting 3 heads (HHH = 1) = $\frac{1}{8}$

Question 10.
A letter is chosen from the word ‘RECTANGLE’. What is the probability that it is
(i) a consonant
(ii) not a consonant.

In the word ‘RECTANGLE’
Total letters (outcomes) = 9
(i) Probability of a letter which is a consonant P(E) = (R, C, T, N, G, L)
$\frac{6}{9}=\frac{2}{3}$
(ii) Probability of a letter being not a consonant (E, A, E), P(E) = $\frac{3}{9}=\frac{1}{3}$.

— End of Data Handling Class-8 ML Aggarwal Solutions :–