CBSE Class 8 Mathematics Data Handling Assignment Set 02

1. A bag has 4 red balls and 2 yellow balls. (The balls are identical in all respect other than colour). A ball is drawn from the bag without looking into the bag. The probability of getting a red ball is ____.
(A) 1/2
(B) 2/3
(C) 1/4
(D) 1/5
Answer : B

DIRECTION (2 - 4) : The histogram representing the marks obtained by 60 students in a Mathematics examination

2. What is the total number of students who obtained more than or equal to 80 marks in the examination?
(A) 13
(B) 3
(C) 8
(D) 11
Answer : D

3. If the minimum pass marks was 40, how many students failed ?
(A) 1
(B) 13
(C) 2
(D) 7
Answer : C

4. How many students were awarded merit, if the minimum marks required for it are 80?
(A) 10
(B) 11
(C) 12
(D) 8
Answer : B

5. A die is thrown. The probability of getting a multiple of 3 is ____.
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
Answer : B

6. From the given table, the number of students who got more than or equal to 50 marks, is ____.

(A) 15
(B) 21
(C) 25
(D) 29
Answer : C

7. The given pie chart gives the marks scored in an examination by a student in English, Hindi, Science & Technology, Social Science and Mathematics. If the total marks obtained by the student were 540, then the subject in which the student scored 105 marks, is______.

(A) English
(B) Mathematics
(C) Social Science
(D) Hindi
Answer : D

8. The probability of occurrence of an event is ____.

Answer : B

9. In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at random.
The probability that the chosen lady dislike coffee is ____.
(A) 59/100
(B) 41/100
(C) 100/59
(D) 100/41
Answer : A

10. The number of times a particular entry occurs in a set of data is known as its
(A) Range
(B) Class-size
(C) Frequency
(D) Class-interval
Answer : C

11. The mid-value of a class-interval is called its
(A) Class-limit
(B) Class-mark
(C) Class-width
(D) Range
Answer : B

DIRECTION (12 - 15) : Study the graph carefully and answer the questions given below it.

12. In which year did the wheat import register highest increase over its preceding year ?
(A) 1973
(B) 1974
(C) 1975
(D) 1978
Answer : C

13. The wheat import in 1976 was approximately how many times to that of the year 1972 ?
(A) 0.31
(B) 1.68
(C) 2.41
(D) 3.22
Answer : D

14. The increase in wheat import in 1978 was what percent of the wheat import in 1977 ?
(A) 25 %
(B) 5 %
(C) 125 %
(D) 80 %
Answer : A

15. The wheat import in 1974 is approximately what percent of the average wheat import for the given years ?
(A) 125 %
(B) 115 %
(C) 190 %
(D) 85 %
Answer : B

16 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 : B

17. 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) 2/5
(B) 1/5
(C) 3/5
(D) 4/5
Answer : A

18. Monthly salary of a person is ` 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) ₹ 5000
(B) ₹ 2500
(C) ₹ 6000
(D) ₹ 9000
Answer : B

19 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) 7/10
(B) 3/10
(C) 4/5
(D) 2/5
Answer : B

20. 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) 7/20
(B) 3/5
(C) 1/5
(D) 1/4
Answer : C

DIRECTION (21-22) : The given pie chart shows the spendings of a family on various heads during a month. Study the graph and answer the questions

21. If the total income of the family is ₹ 25000, then the amount spent on rent and food together is _____.
(A) ₹ 17250
(B) ₹ 14750
(C) ₹ 11250
(D) ₹ 8500
Answer : B

22. What is the ratio of the expenses on education to the expenses on food?
(A) 1 : 3
(B) 3 : 1
(C) 3 : 5
(D) 5 : 3
Answer : A

23. The given bar graph shows the number of students in a hostel speaking different languages. Study the bar graph and answer the following questions.

(i) How many students are there in the hostel?
(ii) What is the ratio of the number of students speaking Punjabi to those speaking English?
(iii) What is the percentage of the students speaking Marathi over those speaking Hindi?
        (i)         (ii)         (iii)
(A) 152       3 : 4       27.9%
(B) 152       4 : 5       25%
(C) 145       7 : 5       27.2%
(D) 145       7 : 9       30%
Answer : C

24. Look at the given below data.
39, 25, 5, 33, 19, 21, 12, 48, 13, 21, 9, 1, 10, 8, 12, 17, 41,40, 12, 46, 37, 17, 27, 30, 6, 2, 23, 19
The frequency distribution of the data is given here

Which of the above tables is the frequency table of the given data?
(A) Only P
(B) Only Q
(C) Neither P nor Q
(D) Can’t be determined
Answer : C

25. The given 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 : D

Data Handling

Questions carrying 1 Mark each :-

Question 1. List the number of outcomes when a coin is tossed.
Answer: There are 2 possible outcomes when a coin is tossed, which are Head (H) and Tail (T).
In simple words: A coin toss has two possible results: getting either a Head or a Tail.

Exam Tip: Always remember that simple random experiments have a fixed and countable set of elementary outcomes.

Question 2. In a bar graph, bars are of equal width but varying height.
Answer: width, height
In simple words: In bar graphs, all bars have the same thickness, but their lengths change based on the numerical value they represent.

Exam Tip: The uniform width ensures visual fairness, while varying heights represent different frequencies or values.

Question 3. A pic chart is also called a circle graph.
Answer: circle graph
In simple words: A pie chart displays data in the form of a circular sector representing proportions.

Exam Tip: Note the spelling variant used in curriculum questions (pic chart / pie chart).

Question 4. In a pie chart, the total sum of all central angles must be 360 degrees.
Answer: \(360^\circ\)
In simple words: The complete angle around the center of a circle is always \(360^\circ\).

Exam Tip: Always verify that the sum of all calculated central sectors equals \(360^\circ\) to check calculation accuracy.

Questions Carrying 2 Mark each:-

Question 5. The marks obtained in Mathematics by 40 students of a class in an examination are 3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 5, 24, 15, 7, 10, 18, 18, 7, 17, 21, 15, 5, 23, 2, 12, 20, 2, 10, 16, 23, 18, 12, 6, 9, 7, 3, 5, 16, 8 and 8. Present the data in the form of a grouped frequency distribution, using class intervals of equal size, one of the class intervals being 5-10.
Answer: Given data size \(N = 40\). The class intervals of equal size 5 are: 0-5, 5-10, 10-15, 15-20, 20-25.
Preparing the frequency distribution table using tally marks:

In simple words: We count how many student marks fall into each range of 5 numbers and tabulate the totals.

Exam Tip: Always double check that the sum of all individual frequencies equals the total number of observations given in the problem statement.

Question 6. Read the bar graph and answer the following questions:-
(i) In which subject maximum number of students got distinction?
(ii) In which subject, the number of distinctions is minimum?
(iii) How many distinctions were obtained by students in a school?
(iv) Write subject in order of the performance.
Answer:
(i) Mathematics (since the bar height is maximum at 8 units).
(ii) Hindi (since the bar height is minimum at 2 units).
(iii) Total distinctions = \(2 + 4 + 8 + 3 + 5 = 22\).
(iv) Order of subjects from best to least performance based on bar heights: Mathematics, Science, English, Social Science, Hindi.
In simple words: We read the tallest and shortest bars from the provided graph to find maximum and minimum values, and sum all values for total distinctions.

Exam Tip: Read axis labels carefully before determining heights corresponding to each category.

Question 7. Two dice are thrown, find and number of outcomes.
Answer: When two dice are thrown simultaneously, the total number of possible outcomes is \(6 \times 6 = 36\).
In simple words: Each die has 6 faces, so rolling two dice gives \(6 \times 6 = 36\) possible pairs of numbers.

Exam Tip: Use the fundamental principle of counting (\(n_1 \times n_2\)) for combined independent events.

Question 8. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a non-red ball?
Answer: Total number of balls = \(2 + 3 + 5 = 10\).
Number of red balls = 2.
Number of non-red balls = Total balls - Red balls = \(10 - 2 = 8\).
Probability of getting a non-red ball = \(\frac{\text{Number of non-red balls}}{\text{Total number of balls}} = \frac{8}{10} = \frac{4}{5} = 0.8\).
In simple words: Subtract the red balls from the total to find non-red balls, then divide by the total number of balls.

Exam Tip: Alternatively, calculate the probability of getting a red ball (\(\frac{2}{10}\)) and subtract it from 1: \(1 - \frac{2}{10} = \frac{8}{10} = \frac{4}{5}\).

Questions carrying 3 marks each :-

Question 9. The data on mode of transport used by students to come to school are as given below:-
Mode of Transport: Bus, Cycle, Train, Car, Scooter
Number of Students: 120, 180, 240, 80, 100
Find the central angle of each sector.
Answer: Total number of students = \(120 + 180 + 240 + 80 + 100 = 730\) Wait, let us re-add correctly: \(120 + 180 = 300\); \(300 + 240 = 540\); \(540 + 80 = 620\); \(620 + 100 = 720\).
Total students = 720.
Central angle formula = \(\left(\frac{\text{Value}}{\text{Total Value}}\right) \times 360^\circ\):
- Bus: \(\left(\frac{120}{720}\right) \times 360^\circ = \frac{1}{6} \times 360^\circ = 60^\circ\)
- Cycle: \(\left(\frac{180}{720}\right) \times 360^\circ = \frac{1}{4} \times 360^\circ = 90^\circ\)
- Train: \(\left(\frac{240}{720}\right) \times 360^\circ = \frac{1}{3} \times 360^\circ = 120^\circ\)
- Car: \(\left(\frac{80}{720}\right) \times 360^\circ = \frac{1}{9} \times 360^\circ = 40^\circ\)
- Scooter: \(\left(\frac{100}{720}\right) \times 360^\circ = \frac{5}{36} \times 360^\circ = 50^\circ\)
Check sum of angles: \(60^\circ + 90^\circ + 120^\circ + 40^\circ + 50^\circ = 360^\circ\).
In simple words: Find the fraction of students for each transport type and multiply by \(360^\circ\) to find its pie slice angle.

Exam Tip: Always verify that all calculated central angles add up exactly to \(360^\circ\).

Question 10. A coin and a die are thrown simultaneously. Find the number of possible outcomes also, name the outcomes.
Answer: Number of outcomes for a coin = 2 (Head, Tail).
Number of outcomes for a die = 6 (1, 2, 3, 4, 5, 6).
Total number of possible outcomes = \(2 \times 6 = 12\).
Names of outcomes:
\((H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)\)
\((T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)\)
In simple words: Pairing each coin result (Head/Tail) with each die number gives 12 unique combinations.

Question 11. Marks secured by a student in various subjects in an examination are:
Subject: Hindi, English, Maths, Soc. Science, Gen. Science
Marks: 40, 52, 80, 70, 75
Answer: To represent this data or analyze it, let us find the central angle for each subject to construct a pie chart or bar representation.
Total marks = \(40 + 52 + 80 + 70 + 75 = 317\).
Central angles:
- Hindi: \(\left(\frac{40}{317}\right) \times 360^\circ \approx 45.42^\circ\)
- English: \(\left(\frac{52}{317}\right) \times 360^\circ \approx 59.05^\circ\)
- Maths: \(\left(\frac{80}{317}\right) \times 360^\circ \approx 90.85^\circ\)
- Soc. Science: \(\left(\frac{70}{317}\right) \times 360^\circ \approx 79.49^\circ\)
- Gen. Science: \(\left(\frac{75}{317}\right) \times 360^\circ \approx 85.17^\circ\)
In simple words: Calculate each subject's proportion out of total marks and convert into degree angles for graphical display.

Exam Tip: For 6-mark questions involving tables, clearly show all intermediate calculation steps.

Question 12. The following data shows the expenditure of an individual over various items:
Items: Education, Food, Rent, Clothing, Others
Expenditure (in Rs.): 1600, 3200, 4000, 2400, 3200
Represent the above data by a pie chart.
Answer: Total expenditure = \(1600 + 3200 + 4000 + 2400 + 3200 = 14400\) Rs.
Calculating central angles \(\left(\frac{\text{Item Expenditure}}{14400}\right) \times 360^\circ\):
- Education: \(\left(\frac{1600}{14400}\right) \times 360^\circ = \frac{1}{9} \times 360^\circ = 40^\circ\)
- Food: \(\left(\frac{3200}{14400}\right) \times 360^\circ = \frac{2}{9} \times 360^\circ = 80^\circ\)
- Rent: \(\left(\frac{4000}{14400}\right) \times 360^\circ = \frac{5}{18} \times 360^\circ = 100^\circ\)
- Clothing: \(\left(\frac{2400}{14400}\right) \times 360^\circ = \frac{1}{6} \times 360^\circ = 60^\circ\)
- Others: \(\left(\frac{3200}{14400}\right) \times 360^\circ = \frac{2}{9} \times 360^\circ = 80^\circ\)
Sum of angles = \(40^\circ + 80^\circ + 100^\circ + 60^\circ + 80^\circ = 360^\circ\).
In simple words: Find each expense's fraction of the total budget, multiply by \(360^\circ\), and draw sectors using a protractor.

Exam Tip: Draw a circle of convenient radius with a compass, then use a protractor to mark each central angle sequentially.

Question 13. Draw a histogram for the following data:
Class Interval: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
Frequency: 5, 10, 7, 9, 12, 13
Answer: To draw a histogram for continuous grouped data:
1. Take class intervals along the horizontal axis (X-axis) on a suitable scale.
2. Take frequencies along the vertical axis (Y-axis) on a suitable scale.
3. Construct adjacent rectangular bars where the width represents the class interval size (10) and the height represents the respective frequency (5, 10, 7, 9, 12, 13).
In simple words: A histogram looks like a bar graph, but with no spaces between bars because data intervals are continuous.

Exam Tip: Remember to mark a kink (jagged break line) on the X-axis if the scale does not start at 0 (since intervals start at 10).

Multiple choice Questions carrying 1 mark each:

Question 14. The sum of all central angles in a pie chart is:
(a) \(9^\circ\)
(b) \(360^\circ\)
(c) \(0^\circ\)
(d) None of the options
Answer: (b) \(360^\circ\)
The complete angle around a point is always \(360^\circ\).
In simple words: A full circle measures \(360^\circ\).

Exam Tip: Memorize standard circle properties for quick MCQ scoring.

Question 15. When a die is thrown, total number of possible outcomes are:
(a) 2
(b) 36
(c) 6
(d) 9
Answer: (c) 6
A standard die has 6 faces numbered 1 through 6.
In simple words: A single die has 6 possible numbers: 1, 2, 3, 4, 5, and 6.

Exam Tip: Do not confuse a single die (6 outcomes) with two dice (36 outcomes).