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Important Questions for CBSE Class 8 Maths Chapter 5 - Data Handling

CBSE

Important Questions for CBSE Class 8 Maths Chapter 5 - Data Handling

Last updated date: 26th Apr 2024

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CBSE Class 8 Maths Important Questions for Data Handling - Free PDF Download

CBSE Class 8 Maths Chapter 5 Data Handling is an important part of this syllabus that teaches students how to organise data and how to extract specific information according to the questions asked. To study this chapter well, download and solve the important questions framed by the experts by following the latest CBSE Class 8 Maths syllabus. Take your preparation to the next level by using these problems as a learning platform.

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Study Important Questions for Class 8 Maths Chapter 5 - Data Handling

Very Short Answer Type Questions (1 Mark)

1. Collections of Observations are called _______

Ans: Data

2. Difference between highest and lowest values of Observations in a data is called

_______ of the data.

Ans: Range

3. The number of times a particular observation occurs in a given data is called

________

Ans: Frequency

4. Define class size.

Ans: The difference between the upper limit and lower limit of a class interval is called

class size.

5. ________ is a pictorial representation of numerical data in the form of rectangle

(bars) of equal width and varying lengths.

Ans:Bar Graph

6. An operation which produce some well defined outcomes is called an _______

Ans: Random Experiment

7. Each outcome of an experiment is called ________

Ans: Trial

Short Answer Type Questions (2 Marks)

1. Define a random experiment and a trial

Ans: An experiment in which all possible outcomes are already known and the exact outcome cannot be predicted in advance is called a random experiment.

Trial means performing a random experiment.

2. Define probability of occurrence of an event.

Ans: Let \[{\text{E}}\] be an event, then the probability of occurrence of \[{\text{E}}\] is defined as,

${\text{P(E)}} = \dfrac{{{\text{ Number of outcomes favourable to E}}}}{{{\text{ Total number of possible outcomes }}}}$

3. A coin is tossed. What is the probability of getting a tail?

Ans: When a coin is tossed the possible outputs are \[{\text{H, T}}\].

The probability of getting a tail is $\dfrac{1}{2}$.

4. In a deck of \[52\] cards, what is the probability of getting

(a) Black cards

Ans:Total black cards $ = 26$

The probability of getting Black cards is,

${\text{P(E)}} = \dfrac{{26}}{{52}}$

(b) Red cards

Ans: Total Red cards $ = 26$

The probability of getting Red cards is,

${\text{P(E)}} = \dfrac{{26}}{{52}}$

Ans: Total Face cards $ = 12$

The probability of getting Face cards is,

${\text{P(E)}} = \dfrac{{12}}{{52}}$

5. When a die is thrown what is the probability of getting prime?

Ans: The possible outcomes when a die is thrown are $1,2,3,4,5,6 = 6$ outcomes the prime numbers are \[2,3,5\].

The possibility of getting prime numbers ${\text{P(E)}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Short Answer Type Questions (3 Mark)

1. Define class intervals, upper limit and lower limit with examples.

Ans: When the number of observations is large, the data is usually organized into graphs called class interval.

The lower value of a class interval is called the lower limit and upper value of class interval is called the upper limit.

Example: \[40{\text{ }} - {\text{ }}45\]class interval

Lower limit $ - \,\,40$

Upper limit $ - \,\,45$

2. Explain the components of a well shuffled deck of \[52\] cards.

Ans: A deck of playing cards has in all \[52\] cards,

(i) It has \[13\] cards, each \[4\] suits namely spades, clubs, hearts and diamonds.

(ii) Cards of spades and cubes are black cards.

(iii) Cards of hearts and diamonds are red cards.

(iv) Kings, Queen and Jacks are known as face cards. Thus, these are in all \[12\] face cards.

3. Out of 45 students in a class 30 are boys and 15 are girls. If chosen randomly what

is the probability that the student is a

(a) boy

Ans: Total number of students $ = 45$

The probability of the student is boy $ = \dfrac{{30}}{{45}} = \dfrac{2}{3}$.

(b) girl

Ans:Total number of students $ = 45$

The probability of the student is girl $ = \dfrac{{15}}{{45}} = \dfrac{1}{3}$.

4. A die is thrown once. What is the probability of

(a) number being less than \[1\]

Ans:Total possible outcomes $ = 1,2,3,4,5,6$

Number being less than $1 = = \dfrac{0}{6} = 0$.

(b) Number being greater than \[{\mathbf{3}}\]

Ans:Total possible outcomes $ = 1,2,3,4,5,6$

Number being greater than $3 = \dfrac{3}{6} = \dfrac{1}{2}$.

Long Answer Type Questions (4 Marks)

1. The below is the data of height of different players recorded. Arrange the data in ascending order and state the frequency of each observation and prepare frequency

table.

$120\;{\text{cm}},100\;{\text{cm}},110\;{\text{cm}},109\;{\text{cm}},100\;{\text{cm}},108\;{\text{cm}},100\;{\text{cm}},110\;{\text{cm}},109\;{\text{cm}},120\;{\text{cm}},108\;{\text{cm}}$,

$107\;{\text{cm}},102\;{\text{cm}},101\;{\text{cm}},150\;{\text{cm}},110\;{\text{cm}},108\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}}$.

Ans: Ascending order: $100\;{\text{cm}},100\;{\text{cm}},100\;{\text{cm}},101\;{\text{cm}},102\;{\text{cm}},107\;{\text{cm}},108\;{\text{cm}},108\;{\text{cm}},108\;{\text{cm}}$,$109\;{\text{cm}},110\;{\text{cm}},110\;{\text{cm}},110\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},120\;{\text{cm}},150\;{\text{cm}}$

Heights (cm)	Frequency
\[100\]	\[3\]
\[101\]	\[1\]
\[102\]	\[1\]
\[107\]	\[1\]
\[108\]	\[3\]
\[109\]	\[1\]
\[110\]	\[3\]
\[120\]	\[6\]
\[120\]	\[1\]

2. When three coins are tossed simultaneously, what are all the possible outcomes?

Ans: When three coins are tossed simultaneously the possible outcomes are,

\[{\text{HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}}\]

What is the probability of getting

(a) all tails

Ans: The probability of getting all tails $ = \dfrac{1}{8}$.

(b) at least one head.

Ans: The probability of getting at least one head $ = \dfrac{7}{8}$.

Long Answer Type Questions (5 Marks)

1. Given below are the $\% $ of attendance obtained by \[20\] students:

\[87,58,80,36,90,92,98,100,84,85,23,52,60,74,89,91,93,87,24,100.\]

Ans: Ascending order $ - 23,24,36,52,58,60,74,80,84,85,87,87,89,90,91,92,93,100,100$

Arrange the data in ascending order and find

(a) Lowest attendance

Ans: Lowest attendance is $23\% $.

(b) Highest attendance

Ans: Highest attendance is $100\% $.

Ans: Range $ = 100 - 23 = 77\% $

2. Draw a Bar Graph for the data given below:

School Supplies	Clip Board	Crayon	Folder	Highlighter	Notebook	Binder
Items Sold	\[6\]	\[7\]	\[7\]	\[9\]	\[12\]	\[14\]

Scale: $x$ Axis $ = 1\;{\text{cm}}\,{\text{ = }}\,1$ item, $y$ axis $ = 1\;{\text{cm}} = 1$ item

Ans:

Bar graph showing items sold by school supplies

3. The bar graph given below shows the sales of books (in thousand number) from six branches of a publishing company during two consecutive years \[2000{\text{ and }}2001.\]

Bar graph showing Export and import of a country

a) What is the ratio of the total sales of branch ${\text{B}}2$ for both years to the total sales of branch \[{\text{B4}}\] for both years?

Ans:Required ratio $ = \dfrac{{(75 + 65)}}{{(85 + 95)}} = \dfrac{{140}}{{180}} = \dfrac{7}{9}$.

b) Total sales of branch ${\text{B}}6$ for both the years is what percent of the total sales of branches ${\text{B}}3$ for both the years?

Ans: Required percentage $ = \left[ {\dfrac{{(70 + 80)}}{{(95 + 110)}} \times 100} \right]\% $

$ = \left[ {\dfrac{{150}}{{205}} \times 100} \right]\% $

$ = 73.17\% .$

c) What percent of the average sales of branches ${\text{B}}1,\;\,{\text{B}}2$ and ${\text{B}}3$ in 2001 is the average

sales of branches \[{\text{B1, B3}}\]and \[{\text{B6}}\]in \[2000?\]

Ans: Average sales (in thousand number) of branches \[{\text{B1, B3 and B6 in 2000}}\]$ = \dfrac{1}{3} \times (80 + 95 + 70) = \left( {\dfrac{{245}}{3}} \right).$

Average sales (in thousand number) of branches \[{\text{B1, B2 and B3 in 2001}}\]

$ = \dfrac{1}{3}{\text{x}}(105 + 65 + 110) = \left( {\dfrac{{280}}{3}} \right)$.

Thus, Required percentage $ = \left[ {\dfrac{{245/3}}{{280/3}} \times 100} \right]\% = \left( {\dfrac{{245}}{{280}} \times 100} \right)\% = 87.5\% $.

d) What is the average sales of all the branches (in thousand numbers) for the year

\[2000?\]

Ans: Average sales of all the six branches (in thousand numbers) for the year \[2000\]

$ = \dfrac{1}{6}{\text{x}}[80 + 75 + 95 + 85 + 75 + 70]$

$ = 80$.

e) Total sales of branches ${\text{B}}1,\;\,{\text{B}}3$ and ${\text{B}}5$ together for both the years (in thousand

numbers) is?

Ans: Total sales of branches ${\text{B}}1,\,\;{\text{B}}3$ and ${\text{B}}5$ for both the years (in thousand numbers)

$ = (80 + 105) + (95 + 110) + (75 + 95)$

$ = 560$

4. Construct a pie chart for the data given below:

Method of Travel	Walk	Bike	Car	Bus
Frequency	\[9\]	\[3\]	\[6\]	\[12\]

Ans:

Method of travel	Frequency	Percent frequency	Angle
Walk	\[9\]	\[\dfrac{9}{{30}} \times 100 = 30\]	\[9 \times \dfrac{{360}}{{30}} = {108^\circ }\]
Bike	\[3\]	\[\dfrac{3}{{30}} \times 100 = 10\]	\[3 \times \dfrac{{360}}{{30}} = {36^\circ }\]
Car	\[6\]	\[\dfrac{6}{{30}} \times 100 = 20\]	\[6 \times \dfrac{{360}}{{30}} = {72^\circ }\]
Bus	\[12\]	\[\dfrac{{12}}{{30}} \times 100 = 40\]	\[12 \times \dfrac{{360}}{{30}} = {144^\circ }\]
Total	\[30\]	\[100\]	\[{360^\circ }\]

The pie chart is,

5. Answer the questions using the data from the pie chart given below:

Pie Chart showing the 2000 Haryana State Expenditure distribution

a) Approximately how many degrees should be there in the central angle of the sector for agriculture expenditure?

Ans:In a pie chart, $100\% $ is spread over ${360^\circ }.$

Therefore $1\% = {3.6^\circ }.$

Agriculture expenditure $ = 59\% $.

Then, $3.6 \times 59 = {212.4^\circ }$.

Therefore, ${212.4^\circ }$ should be there in the central angle of the sector for agriculture expenditure.

b) Approximately what is the ratio of expenditure on agriculture to that on dairy?

Ans:Over here, one common mistake is that students calculate the actual values of agriculture and dairy. Since budget expenditure is proportional to $\% $ of area covered, ratio of agriculture to dairy expenditure would be the ratio of corresponding $\% $ allocations.

Therefore, $\dfrac{{{\text{Agriculture}}}}{{{\text{Diary}}}} = \dfrac{{59}}{6}$.

c) In Haryana, in \[2000\] , a total expenditure of Rs. $120\,{\text{mn}}$ was incurred. Approximately How many million did the Haryana government spend on roads?

Ans:Total expenditure $ = 100\% = $ Rs. $120\,{\text{mn}}.$

Expenditure on roads $ = 9\% = \dfrac{9}{{100}} \times 120 = {\text{Rs}}$. $10.8\,{\text{mn}}$.

Therefore, the Haryana government spend on roads about Rs. $10.8\,{\text{mn}}$.

d) If Rs. $9\,{\text{mn}}$ were spent in \[2000\] on Dairy, what would have been the total expenses in that year in million?

Ans: $9\,{\text{mn}}$ were spent on dairy.

This amount represents $6\% $ of total expenditure in the year \[2000.\]

$6 = $\[\left( {\dfrac{{{\text{Dairy expenditure}}}}{{{\text{Total expenditure}}}}} \right)\]$ \times 100$

$6 = \left( {\dfrac{{\text{9}}}{{{\text{Total}}\,{\text{expenditure}}}}} \right) \times 100$

Total expenditure $ = 100 \times \dfrac{9}{6} = $ Rs. $150\,{\text{mn}}$

Therefore, the total expenses in that year in million is Rs. $150\,{\text{mn}}$.

Importance of CBSE Class 8 Maths Chapter 5 Data Handling Important Questions

These important questions have been formulated by experts to focus on the concepts of data handling. This chapter holds immense importance in the development of the conceptual foundation of the students. Hence, the important questions will become integral to the practice sessions to develop this foundation. The solutions to these important questions are also provided so students can easily resolve their doubts.

Benefits of CBSE Class 8 Maths Chapter 5 Data Handling Important Questions

These important questions can be accessed online or downloaded easily and for free. It will help you make your practice sessions more productive.
The solutions will help you resolve doubts on your own.
Focus on how the experts have solved these problems in the solutions and follow the same to score more in the exams.

Download CBSE Class 8 Maths Chapter 5 Data Handling Important Questions PDF

Get the free PDF version of these important questions and answers to complete your study material for this chapter. Learn how to use the concepts of this chapter to formulate precise answers and proceed with your preparation. Practise and develop your concepts well to stay ahead of the competition.

Importances of CBSE Class 8 Important Questions of Chapter 5- Data Handling

The importance of "Important Questions for CBSE Class 8 Maths Chapter 5 - Data Handling" cannot be overstated, as they play a crucial role in a student's mathematical education. Firstly, these questions provide a structured approach to learning the principles of data handling, a skill set that is increasingly relevant in our data-driven world. By engaging with these questions, students not only gain a solid understanding of data collection and organisation but also develop critical thinking abilities as they analyse, interpret, and draw meaningful conclusions from data.

Secondly, these important questions prepare students for examinations by covering a wide spectrum of topics within data handling. They offer a comprehensive review of the chapter's content, ensuring that students are well-equipped to excel in assessments . These questions encourage practical application of mathematical concepts. They challenge students to solve real-world problems, fostering an appreciation for the practicality and relevance of data analysis in various fields, from science to business.

Conclusion

"Important Questions for CBSE Class 8 Maths Chapter 5 - Data Handling" serve as a valuable resource in a student's mathematical journey. This chapter lays the foundation for essential data analysis skills, equipping students with the ability to collect, organise, and interpret data effectively. The questions presented challenge students to apply their knowledge to real-world scenarios, fostering critical thinking and problem-solving abilities. Moreover, these questions prepare students for examinations by covering a wide range of topics within data handling. They empower learners to become data-literate individuals capable of making informed decisions and finding practical applications for data analysis in various fields.

FAQs on Important Questions for CBSE Class 8 Maths Chapter 5 - Data Handling

1. What are the benefits of solving the Important Questions for CBSE Class 8 Maths Chapter 5-Data Handling?

Benefits of solving the Important Questions for CBSE Class 8 Maths Chapter 5-Data Handling

These significant questions are readily available online or can be downloaded for nothing. It will enable you to increase the effectiveness of your practise sessions.
You can clear up your own doubts with the solutions.
To achieve higher exam scores, pay close attention to how the professionals tackled these issues in the solutions and emulate their methods.

2. How can I improve my data handling skills?

Concentrate on the approaches that the chapter thoroughly explains. Check your answers after completing the exercise questions. Answer the crucial questions to help us assess your knowledge and data-handling abilities. You can advance and hone such skills in this way.

3. What is the Importance of CBSE Class 8 Maths Chapter 5 Data Handling Important Questions?

Experts developed these crucial queries to concentrate on the ideas of data handling. This chapter is crucial to the students' development of their conceptual foundation. As a result, the crucial questions will be included in the practise sessions to build this base. In order to help students clear up any remaining questions, the answers to these crucial questions are also offered.

4. What are a trial and a random experiment?

A random experiment is one in which all potential outcomes are known in advance but the precise result cannot be anticipated. Trial entails doing an experiment at random.

5. Why choosing the NCERT solutions for CBSE Class 8 Maths Chapter 5: Data Handling provided by Vedantu is thought to be a wise choice?

Vedantu is regarded as a viable alternative because the questions in CBSE Class 8 Maths Chapter 5: Data Handling may be answered with conceptual clarity. Students may readily comprehend the types of questions that may be given from this chapter in the test with the aid of these solutions, which will help them achieve high marks.