RBSE Maths Chapter 16 – Data Handling Class 8 Important questions and solutions can be accessed here. The important questions and solutions of Chapter 16, available at BYJU’S, contain detailed step by step explanations. All these important questions are based on the new pattern prescribed by the RBSE. Students can also get the syllabus and textbooks on RBSE Class 8 solutions.
Chapter 16 of the RBSE Class 8 Maths will help the students to solve problems related to the histogram, frequency distribution table using tally marks, bar graph, pie chart, problems on diagrammatic representation of data, probability of events.
RBSE Maths Chapter 16: Exercise 16.1 Textbook Important Questions and Solutions
Question 1: Which of the following types of data will need a histogram?
(i) Quantity of different types of cereals available at home.
(ii) Height of all students at your school.
(iii) The number of cars manufactured by 5 companies.
(iv) The number of vehicles passing a busy crossroad between 8:00 A.M. and 2:00 PM.
(v) Distance between home to the school of all students of your class. (in metres)
Solution:
A histogram is used to show the data of (ii), (iv) and (v).
Question 2: Rakesh distinguishes his clothes on the basis of colours and indicates like this – White (W), Red (R), Black (B), Yellow (Y) and Others (X). The list formed is as follows R, R, X, W, R, B, Y, R, B, W, W, X, X, R, B, Y, Y, X, W, R, B, Y, Y, B, R, R, X, W, W, R, W, X, X, R, Y, W, B, Y, X, X. Using tally marks form a frequency distribution table. To represent it use a bar graph.
Solution:
Frequency distribution table
Colour 
Tally Marks 
Number of clothes 
W 

8 
R 

10 
B 

6 
Y 

7 
X 

9 
Total 
40 
Bar graph
Question 3: Payment of the wages for a week in rupees to 30 NREGA workers of Khatwara village are as follows:
830, 835, 890, 810, 815, 816, 814, 845, 898, 890, 819, 860, 832, 817, 855, 845, 804, 808, 812, 816, 885, 835, 815, 812, 878, 840, 868, 890, 806, 828.
Prepare a frequency distribution table having class intervals as 800 – 810, 810 – 820 using tally marks. Draw a histogram using the table.
Solution:
Frequency Distribution Table
Wages 
Tally Marks 
Number of labourers 
800 – 810 
 
3 
810 – 820 

10 
820 – 830 
 
1 
830 – 840 
 
4 
840 – 850 
 
3 
850 – 860 
 
1 
860 – 870 
 
2 
870 – 880 
 
1 
880 – 890 
 
1 
890 – 900 
 
4 
Total 
30 
Histogram
Question 4: The number of mobiles sold in 30 days by Ms Raja electronics
222, 228, 238, 215, 225, 219, 217, 230, 218, 237, 214, 210, 235, 222, 220, 214, 212, 220, 237, 212, 238, 218, 210, 216, 217, 234, 233, 237, 219, 239.
Prepare a frequency distribution table having class interval as 210 – 215, 215 – 220 using tally marks. Draw a histogram using a table and answer the following questions.
(i) The number of mobiles sold in which class interval is maximum?
(ii) On how many days 230 or more mobiles were sold?
(iii) On how many days less than 230 or more than 230 mobiles were sold?
Solution:
Wages 
Tally Marks 
Number of labourers 
210 – 215 

6 
215 – 220 

8 
220 – 225 
 
2 
225 – 230 
 
3 
230 – 235 
 
4 
235 – 240 

7 
Total 
30 
Histogram
(i) The class interval 215 – 220 has the greatest frequency.
(ii) In 3 + 7 = 10 days, 230 or more mobiles are sold.
(iii) In 6 + 8 + 4 + 2 = 20 days, less than 230 mobiles are sold.
Question 5: In holidays the number of study hours every day of students of class 8 is shown in the graph.
Answer the following questions.
(i) How many hours did most of the students study?
(ii) How many students studied for 5 or less than 5 hours?
(iii) How many students studied during vacations?
(iv) Frequency of which class interval is maximum?
Solution:
(i) Maximum students studied for 4 – 5 hours.
(ii) Number of students who studied for 5 or less than 5 hours = 0 + 8 + 20 + 28 = 60.
(iii) Number of students who studied during the holidays = 4 + 8 + 20 + 28 + 16 + 24 = 100.
(iv) The class interval 4 – 5 has the maximum frequency.
RBSE Maths Chapter 16: Exercise 16.2 Textbook Important Questions and Solutions
Question 1: Number of textbooks of a school is given below. Represent this data through a pie chart.
Subject 
Science 
Maths 
English 
Hindi 
Social Science 
Total 
Books 
200 
120 
190 
170 
40 
720 
Solution:
Subject 
Number of books 
Number of parts in total 
Angle formed 
Science 
200 
200 / 720 = 5 / 18 
[5 / 18] * 360^{o} = 100^{o} 
Maths 
120 
120 / 720 = 1 / 6 
[1 / 6] * 360^{o} = 60^{o} 
English 
190 
190 / 720 = 19 / 72 
[19 / 72] * 360^{o} = 95^{o} 
Hindi 
170 
170 / 720 = 17 / 72 
[17 / 72] * 360^{o} = 85^{o} 
Social Science 
40 
40 / 720 = 1 /18 
[1 / 18] * 360^{o} = 20^{o} 
Total 
720 
720 / 720 = 1 
360^{o} 
Pie Chart
Question 2: Description of daily activities of a child is as follows. Represent this data in the form of a pie chart.
Time Spent 
School 
Sleep 
Play 
Others 
Hours 
8 
6 
2 
8 
Solution:
Time Spent 
Hours 
Number of parts in total 
Angle formed 
School 
8 
8 / 24 = 1 / 3 
[1 / 3] * 360^{o} = 120^{o} 
Sleep 
6 
6 / 24 = 1 / 4 
[1 / 4] * 360^{o} = 90^{o} 
Play 
2 
2 / 24 = 1 / 12 
[1 / 12] * 360^{o} = 30^{o} 
Others 
8 
8 / 24 = 1 / 3 
[1 / 3] * 360^{o} = 120^{o} 
Total 
24 
1 
360^{o} 
Pie Chart
Question 3: The below pie chart shows marks obtained by a student in various subjects Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by these students is 900, then answer the following questions.
(i) In which subject did the student have 250 marks?
(ii) What is the increase in marks obtained by the student between Mathematics and Hindi when compared to each other?
(iii) Check whether total marks obtained in Social Science and Mathematics is more than the total of marks obtained in English and Hindi?
Solution:
(i) Part of whole = 250 / 900
Part of 360^{o} = [250 / 900] * 360^{o} = 100
Hence, the student has obtained 250 marks in Maths.
(ii) Marks obtained in Maths = 250 Marks
Marks obtained in Hindi = [72^{o} / 360^{o}] * 900 = 180
The difference of marks between Maths and Hindi = 250 – 180 = 70
(iii) Marks obtained in Social Science = [60^{o} / 360^{o}] * 900 = 150
Marks obtained in Maths = 250 Marks
Total marks obtained in Social Science and Maths = 150 + 250 = 400
Marks obtained in English = [48^{o} / 360^{o}] * 900 = 120
Marks obtained in Hindi = 180
Total marks obtained in English and Hindi = 120 + 180 = 300
The sum of the marks obtained in Social Science and Maths is greater than the sum of the marks obtained in English and Hindi.
Question 4: Draw a pie chart showing the following information. The table below shows the games liked by students in the class.
Game 
KhoKho 
Kabaddi 
Football 
Cricket 
Number of students 
5 
6 
7 
18 
Solution:
Game 
Number of students 
Number of parts in a whole 
Angle formed 
KhoKho 
5 
5 / 36 
[5 / 36] * 360^{o} = 50^{o} 
Kabaddi 
6 
6 / 36 = 1 / 6 
[6 / 36] * 360^{o} = 60^{o} 
Football 
7 
7 / 36 
[7 / 36] * 360^{o} = 70^{o} 
Cricket 
18 
18 / 36 = 1 / 2 
[18 / 36] * 360^{o} = 180^{o} 
Total 
36 
1 
360^{o} 
Pie Chart
Question 5: In accordance with Jan Dhan Yojana of the Indian government, the number of accounts opened by the following banks in one month in Kota city is as follows:
Name of the bank 
SBBJ 
SBI 
IDBI 
BOI 
Number of accounts opened 
21000 
18000 
6000 
9000 
Draw a pie chart of the above data.
Solution:
Name of the bank 
Number of accounts opened 
Number of parts in a whole 
Angle formed 
SBBJ 
21000 
21000 / 54000 = 7 / 18 
[7 / 18] * 360^{o} = 140^{o} 
SBI 
18000 
18000 / 54000 = 1 / 3 
[1 / 3] * 360^{o} = 120^{o} 
IDBI 
6000 
6000 / 54000 = 1 / 9 
[1 / 9] * 360^{o} = 40^{o} 
BOI 
9000 
9000 / 54000 = 1 / 6 
[1 / 6] * 360^{o} = 60^{o} 
Total 
54000 
1 
360^{o} 
Pie Chart
Question 6: Various mistakes of automobile drivers are shown in the pie chart.
With the help of pie chart, answer the following questions
(i) Percentage of accidents by driving vehicles with fast speed?
(ii) Due to which mistake of an automobile driver, the maximum accidents took place?
(iii) How many accidents occurred due to driving an automobile in a drunken state?
(iv) How many people underwent an accident due to the disobedience of traffic rules?
Solution:
(i) 26.7%
(ii) 29.9% [Dangerous driving]
(iii) 0.3%
(iv) 10.4%
RBSE Maths Chapter 16: Exercise 16.3 Textbook Important Questions and Solutions
Question 1: What is the probability of getting a head on tossing a coin?
Solution:
The outcomes of tossing a coin are either head or a tail.
Sample space = {H, T}
Probability of getting head
= [Number of favourable outcomes] / [Total number of outcomes]
= [1 / 2]
Question 2: There are 6 white, 11 red and 7 yellow balls in a bag. What is the probability of getting a white ball from the bag?
Solution:
Total balls = 6 + 11 + 7 = 24
Number of white balls = 6
Probability of getting white ball from the bag
= [Number of favourable outcomes] / [Total number of outcomes]
= 6 / 24
= 1 / 4
Question 3: What is the probability of getting a queen from a pack of wellshuffled cards?
Solution:
Total number of cards = 52
Number of queens = 4
Probability of getting a queen
= [Number of favourable outcomes] / [Total number of outcomes]
= 4 / 52
= 1 / 13
Question 4: Find the probability of each belowmentioned event when a dice is thrown.
(i) A prime number
(ii) No prime number
(iii) Number more than 3
(iv) Number not more than 5
(v) An odd number.
Solution:
The total number of outcomes when a dice is thrown = (1, 2, 3, 4, 5, 6)
(i) Total number of favorable outcomes = 3 (2, 3, 5)
Required probability = 3 / 6 = 1 / 2
(ii) Total number of favorable outcomes = 3 (1, 4, 6)
Required probability = 3 / 6 = 1 / 2
(iii) Number of favorable outcomes = 3 (4, 5, 6)
Required probability = 3 / 6 = 1 / 2
(iv) Number of favorable outcomes = 5 (1, 2, 3, 4, 5)
Required probability = 5 / 6
(v) Number of favorable outcomes = 3 (1, 3, 5)
Required probability = 3 / 6 = 1 / 2
Question 5: Number from 1 to 15 is written on 15 different slips (one number on each slip). They are mixed and kept in a box. A slip is taken out without looking into the box. What is the probability of the following?
(i) Obtaining number 5.
(ii) Obtaining a number with two digits.
(iii) Obtaining a number having one digit.
Solution:
Total no. of slips = 15
Total number of outcomes = 15
(i) Probability of getting a number 5
= [Number of favourable outcomes] / [Total number of outcomes]
= 1 / 15
(ii) Total number of favorable events = 6 (10, 11, 12, 13, 14, 15)
Probability of obtaining a number with two digits
= [Number of favourable outcomes] / [Total number of outcomes]
= 6 / 15 = 2 / 5
(iii) Total number of favorable events = 9 (1, 2, 3, 4, 5, 6, 7, 8, 9)
Probability of obtaining a number having one digit
= [Number of favourable outcomes] / [Total number of outcomes]
= 9 / 15 = 3 / 5
RBSE Maths Chapter 16: Additional Questions and Solutions
Question 1: Match the following.
Question 
Answer Choices 
1] Frequency of class 3 – 5 in distribution 4, 8, 3, 6, 7, 2, 3, 5, 9, 4, 6, 5, 5 
A] 5 
2] Range of class interval 5 – 10 
B] 0 
3] Probability of getting 8 when a dice is thrown 
C] ½ 
4] Probability of getting a black card from a pack of 52 cards 
D] 7 
Solution:
1] – D]
2] – A]
3] – B]
4] – C]
Question 2: Write any two properties of a histogram
Solution:
• The class intervals are represented by the horizontal line.
• Length of bars indicates the frequency of class intervals.
Question 3: Write the lower and upper limit of class 10 – 20.
Solution:
Lower limit = 10
Upper limit = 20
Question 4: What is the width or size of a class interval?
Solution:
The difference between the upper limit and the lower limit gives the width or size of the class interval.
Question 5: Define the term frequency.
Solution:
The number of times a value that occurs in the data given is called the frequency of the observation.
Question 6: Draw a pie chart for the following data.
Taste 
Chocolate 
Vanilla 
Other 
Percentage of the students who like the taste 
50 
25 
25 
Solution:
Question 7: There are 4 red balls and 2 yellow balls in a bag. What is the probability of drawing a red ball?
Solution:
Total number of outcomes = 4 + 2 = 6
Number of favourable outcomes = 4
Probability of getting a red ball = [Number of favourable outcomes] / [Total number of outcomes]
= 4 / 6
= 2 / 3
Question 8: Find the probability of getting an even number when a dice is thrown.
Solution:
When a dice is thrown, the total outcomes are = 6 (1, 2, 3, 4, 5, 6)
Even number outcomes = 3 (2, 4, 6)
Probability of getting an even number = [Number of favourable outcomes] / [Total number of outcomes]
= 3 / 6
= 1 / 2
Question 9: Draw a proper graph to represent the following data.
Month 
Number of watches sold 
July 
1000 
August 
1500 
September 
1500 
October 
2000 
November 
2500 
December 
1500 
Solution:
Question 10: Observe the histogram given below and answer the following questions.
(i) Which information is being given by histogram?
(ii) In which class interval the number of girls is maximum?
(iii) How many students are having 145 cm or more height?
(iv) If we divide the girls into three categories, then how many girls will be there in each category?
 150 cm or more – Class A
 Between 140 cm to 150 cm – Class B
 Less than 140 cm – Class C
Solution:
(i) The histogram represents the height of the students (girls) of class VII.
(ii) In the class interval 140 – 145, the number of girls is maximum.
(iii) The number of students whose height is > or = 145 cm are 4 + 2 + 1 = 7.
(iv) In class A = 2 + 1 = 3 girls
In class B, 7 + 4 = 11 girls
In class C,1 + 2 + 3 = 7 girls
Question 11: From the given bar graph, answer the following questions.
(i) Which subject has the maximum number of books and how many?
(ii) Which subject has the least number of books and how many?
(iii) How many books are there in the library?
(iv) What information has been given by this bar graph?
(v) The difference in the number of books of which two subjects is minimum?
Solution:
(i) Hindi = 450
(ii) Social Science = 100
(iii) Total books = 150 + 300 + 350 + 450 + 100 = 1350
(iv) This bar graph represents the number of books of each subject in the library.
(v) Subjects Maths and Science (350 – 300 = 50) and English and Social Science (150 – 100 = 50) have the minimum difference of books.
Question 12: Draw appropriate graphs for the following data.
[i]
Year 
2010 
2011 
2012 
2013 
2014 
Number of books brought for the library 
170 
150 
190 
180 
210 
Name of village 
Makadi 
Akola 
Rawaliya Khurd 
Siwadiya 
Number of men 
1800 
1700 
1800 
1500 
Number of women 
1600 
1700 
1900 
1600 
Solution:
[i][ii]
Question 13: Study the following frequency distribution and answer the following questions.
Class interval 
Frequency 
100 – 150 
45 
150 – 200 
25 
200 – 250 
55 
250 – 300 
125 
300 – 350 
140 
350 – 400 
65 
400 – 450 
45 
Total 
500 
(i) What is the measure of class interval?
(ii) Which is the upper limit of the class interval 300 – 350?
(iii) Frequency of which group is maximum?
(iv) Frequency of which two groups is the same?
Solution:
(i) Class size 150 – 100 = 50
(ii) 350
(iii) 300350
(iv) 100 – 150 and 400 – 450