## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions

**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 ………..

Solution:

(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.

Solution:

(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’e 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**

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

Three coins are tossed,

then total number of outcomes = 2^{3} = 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’

Solution:

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

Solution:

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) \(\frac{1}{2}\)

Solution:

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

Solution:

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**

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?

Solution:

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?

Solution:

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?

Solution:

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)**

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.

Solution:

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?

Solution:

Ankita and Nagma both born in 1998.

(i) Probability of being same birth date = \(\frac{1}{365}\).

(ii) Probability of being different birth dates = \(\frac{365-1}{365}=\frac{364}{365}\).