**NCERT Solutions for Class 8 Maths Chapter 5 Data Handling** is crucial for the students of 8th class to clear their doubts and excel in their examination. These solutions help students to gain a better understanding of the topic. BYJU’S provides these NCERT Solutions to help the students not only to sort their difficulties in solving problems, but also to develop a deeper understanding of the related concepts and to ease the fear of Maths.

Students can also download PDF of NCERT Class 8 Maths Solutions for Data Handling Chapter 5 or can view it online by following the links. Data Handling is an important concept that assures the uprightness of the research data. We have information in the form of a numerical figure, no matter which field we take. Every value of this kind is known as an observation. Usually, the set of all the observation is called data. Different data management methods are used to handle, termed as data, which will be discussed in this chapter as well as in the higher classes. These solutions for Data handling are designed by subject experts, as per the CBSE syllabus for the year 2020-21, prescribed by the board itself.

### Download PDF of NCERT Solutions for Class 8 Maths 5- Data Handling

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## Exercise 5.1 Page: 76

**1. For which of these would you use a histogram to show the data?**

** (a) The number of letters for different areas in a postman’s bag.**

**(b) The height of competitors in an athletics meet.**

**(c) The number cassettes produced by 5 companies.**

**(d) The number of passengers boarding trains from 7.00 a.m. to 7.00 p.m. at a station. Give reason for each.**

Solution:

We know that Histogram is a graphical representation of data if the data represented using class- interval.

Since the cases mentioned in options (b) and (d) can be divided into class intervals, histogram can be used to show the data.

Similarly, since the cases mentioned in options (a) and (c) cannot be divided into class intervals, histogram cannot be used to represent the data.

**2. The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning.**

W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W M W G W M G W M M B G G W.

Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Solution:

Frequency distribution table:

Bar-graph:

**3. The weekly wages (in ₹) of 30 workers in a factory are:**

830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808,

812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.

Using tally marks, make a frequency table with intervals as 800 – 810, 810 – 820 and so on.

Solution:

The frequency table with intervals as 800 – 810, 810 – 820 and so on, using tally marks is given below:

**4. Draw a histogram for the frequency table made for the data in Question 3 and answer the following questions.**

**(i) Which group has the maximum number of workers?**

**(ii) How many workers earn ₹ 850 and more?**

**(iii) How many workers earn less than ₹ 850? **

Solution:

(i) 830-840 is the group having maximum number of workers, 9, compared to other groups.

(ii) Workers earning ₹ 850 and more= 1+3+1+1+4=10

(iii) Workers earning less than ₹ 850= 3+2+1+9+5=20

**5. The number of hours for which students of a particular class watched television during holidays is shown through the given graph.**

Answer the following:

**(i) For how many hours did the maximum number of students watch T.V.?**

**(ii) How many students watched TV for less than 4 hours?**

**(iii) How many students spent more than 5 hours in watching TV?**

Solution:

(i) 32 students watched T.V for 4-5 hours. ∴, The maximum number of students who watched T.V. for 4 – 5 hours.

(ii) The number of students who watched T.V. less than 4 hours= 22+8+4=34

(iii) The number of students who spent more than 5 hours in watching TV

=8+6=14

## Exercise 5.2 Page: 82

**1. A survey was made to find the type of music that a certain group of young people liked in a city.**

Adjoining pie chart shows the findings of this survey. From this pie chart, answer the following:

**(i) If 20 people liked classical music, how many young people were surveyed?**

**(ii) Which type of music is liked by the maximum number of people?**

**(iii) If a cassette company were to make 1000 CD’s, how many of each type would they**

make?

Solution:

(i) 10% represents 100 people.

⟹20% represents = (100×20)/10 = 200

∴, 200 people were surveyed.

(ii) Since 40% of the total people surveyed liked light music and no other form of song liked more than that, we can conclude that Light music is liked by the maximum number of people.

(iii) CD’s of classical music = (10 × 1000)/100 = 100

CD’s of semi-classical music = (20 × 1000)/100 = 200

CD’s of light music = (40 × 1000)/100 = 400

CD’s of folk music = (30 × 1000)/100 = 300

**2. A group of 360 people were asked to vote for their favorite season from the three**

seasons rainy, winter and summer.

**(i) Which season got the most votes?**

**(ii)Find the central angle of each sector.**

**(iii) Draw a pie chart to show this information**

Solution:

(i) According to the table given in the question, Winter season got the most votes.

(ii) Central angle of summer season= (90×360)/360= 90o

Central angle of rainy season= (120×360)/360= 120o

Central angle of winter season= (150×360)/360= 150o

(iii)

**3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.**

Solution:

Here, central angle = 360o Total number of people = 36

**4. The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.**

**(i) In which subject did the student score 105 marks?**

(Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)

**(ii) How many more marks were obtained by the student in Mathematics than in Hindi?**

**(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).**

Solution:

(i) The student scored 105 marks in Hindi.

(ii) Marks obtained in Mathematics = 135 Marks obtained in Hindi = 105 Difference = 135 – 105 = 30

Thus, 30 more marks were obtained by the student in Mathematics than in Hindi.

(iii) The sum of marks in Social Science and Mathematics = 97.5 + 135 = 232.5 The sum of marks in Science and Hindi = 120 + 105 = 225

∴, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.

**5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.**

Solution:

NCERT Solution For Class 8 Maths Chapter 5- Data Handling

## Exercise 5.3 Page: 87

**1. List the outcomes you can see in these experiments.**

**(a) Spinning a wheel (b) Tossing two coins together**

Solution:

(a) There are four letters A, B, C and D in a spinning wheel. So there are 4 outcomes.

(b) When two coins are tossed together. There are four possible outcomes HH, HT, TH, TT.

**2. When a die is thrown, list the outcomes of an event of getting**

**(i) (a) a prime number (b) not a prime number.**

**(ii) (a) a number greater than 5 (b) a number not greater than 5.**

Solution:

(i) (a) Outcomes of event of getting a prime number are 2, 3 and 5.

(b) Outcomes of event of not getting a prime number are 1, 4 and 6.

(ii) (a) Outcomes of event of getting a number greater than 5 is 6.

(b) Outcomes of event of not getting a number greater than 5 are 1, 2, 3, 4 and 5.

**3. Find the.**

**(a) Probability of the pointer stopping on D in (Question 1-(a)).**

**(b) Probability of getting an ace from a well shuffled deck of 52 playing cards.**

**(c) Probability of getting a red apple. (See figure below)**

Solution:

(a) In a spinning wheel, there are five pointers A, A, B, C, D. So there are five

outcomes. Pointer stops at D which is one outcome.

So the probability of the pointer stopping on D = 1/5

(b) There are 4 aces in a deck of 52 playing cards. So there are four events of getting an ace.

So, probability of getting an ace = 4/52 = 1/13

(c) Total number of apples = 7

Number of red apples = 4

Probability of getting red apple = 4/7

**4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .**

**(i) getting a number 6?**

**(ii) getting a number less than 6? (iii) getting a number greater than 6? (iv)getting a 1-digit number?**

Solution:

(i) Outcome of getting a number 6 from ten separate slips is one.

∴, probability of getting a number 6 = 1/10

(ii) Numbers less than 6 are 1, 2, 3, 4 and 5 which are five. So there are 5 outcomes.

∴, probability of getting a number less 6 =5/10 = ½

(iii)Number greater than 6 out of ten that are 7, 8, 9, 10. So there are 4 possible outcomes.

∴, probability of getting a number greater than 6 = 4/10 = 2/5

(iv) One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 out of ten.

∴, probability of getting a 1-digit number = 9/10

**5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector?**

Solution:

A total of five sectors are present.

Out of the five sectors, three sectors are green.

∴, probability of getting a green sector = 3/5

Out of the five sectors, one sector is blue. Hence, Non-blue sectors = 5 – 1 = 4 sectors

∴, probability of getting a non-blue sector= 4/5

**6. Find the probabilities of the events given in Question 2.**

Solution:

When a die is thrown, there are total six outcomes, i.e., 1, 2, 3, 4, 5 and 6.

(i)

(a) 2, 3, 5 are the prime numbers. So there are 3 outcomes out of 6.

∴,probability of getting a prime number =3/6 = ½

(b) 1, 4, 6 are not the prime numbers. So there are 3 outcomes out of 6.

∴,probability of getting a prime number =3/6 = ½

(ii)

(c) Only 6 is greater than 5.

So there is one outcome out of 6.

∴,probability of getting a number greater than 5= 1/6

(d) Numbers not greater than 5 are 1, 2, 3, 4 and 5. So there are 5 outcomes out of 6.

∴,probability of not getting a number greater than 5= 5/6

Also Access |

NCERT Exemplar for Class 8 Maths Chapter 5 |

CBSE Notes for Class 8 Maths Chapter 5 |

## NCERT Solutions for Class 8 Maths Chapter 5- Data Handling

Solving the NCERT Solutions for Class 8 is very important from the CBSE board examination point of view. Data Handling is one of the chapters in Class 8 Maths that contains the concepts that are likely to be used in daily life. The chapter deals with different concepts related to Data Handling. Let us have a look at some of them.

- Data mostly available to us in an unorganised form is called raw data.
- In order to draw meaningful inferences from any data, we need to organise the data systematically.
- Frequency gives the number of times that a particular entry occurs.
- Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.
- Grouped data can be presented using a histogram. The histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
- Data can also be presented using a circle graph or pie chart. A circle graph shows the relationship between a whole and its parts.
- There are certain experiments whose outcomes have an equal chance of occurring.
- A random experiment is one whose outcome cannot be predicted exactly in advance.
- Outcomes of an experiment are equally likely if each has the same chance of occurring. Probability of an event = Number of outcomes that make an event Total number of outcomes of the experiment, when the outcomes are equally likely.
- One or more outcomes of an experiment make an event.
- Chances and probability are related to real life.

Main topics covered in this chapter include:

5.1 Looking for Information

5.2 Organising Data

5.3 Grouping Data

5.3.1 Bars with a difference

5.4 Circle Graph Or Pie Chart

5.4.1 Drawing pie charts

5.5 Chance and Probability

5.5.1 Getting a result

5.5.2 Equally likely outcomes

5.5.3 Linking chances to probability

5.5.4 Outcomes as events

5.5.5 Chances and Probability related to real life.

Exercise 5.1 Solutions 5 Questions (5 Short Answer Questions)

Exercise 5.2 Solutions 5 Questions (3 Long Answer Questions and 2 Short Answer Questions)

Exercise 5.3 Solutions 6 Questions (2 Long Answer Questions and 4 Short Answer Questions)

## NCERT Solutions for Class 8 Maths Chapter 5- Data Handling

Information that we collect in our day to day life is called Data. The graphical representation of the data collected gives a clear idea of what it represents. The different types of graphs used to represent the data include pictograph, bar graph, double bar graph, pie charts, etc. Chapter 5 of Class 8 Maths, Data handling deals with organising data and grouping the data. The data can be grouped using the frequency distribution table. In this chapter, the students also learn about the chances or probability of an event as well as how these probabilities can be represented.

Studying Chapter 5 of Class 8, Data Handling helps the students in:

- Reading bar-graphs, ungrouped data, arranging it into groups, representation of grouped data through bar-graphs, constructing and interpreting bar-graphs.
- Simple pie charts with reasonable data numbers.
- Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to chance in life events.
- Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice.
- Throwing a large number of identical dice/coins together and aggregating the result of the throws to get large number of individual events.
- Observing the aggregating numbers over a large number of repeated events.
- Comparing with the data for a coin.
- Observing strings of throws, notion of randomness.

**Disclaimer:**

**Dropped topics –** 5.2 Organising Data, 5.3 Grouping Data and 5.3.1 Bars with difference.

## Frequently Asked Questions on NCERT Solutions for Class 8 Maths Chapter 5

### Where can I get the accurate solution for NCERT Solution for Class 8 Maths Chapter 5?

At BYJU’S you can get the accurate solution in PDF format for NCERT Solution for Class 8 Maths Chapter 5. The NCERT Textbook Solutions for this chapter have been designed accurately by mathematics experts at BYJU’S. All these solutions are provided by considering the new pattern of CBSE, so that students can get thorough knowledge for their exams.

### Is it necessary to solve each problem provided in the NCERT Solution for Class 8 Maths Chapter 5?

Yes. Because these questions are important from an exam perspective. These questions are solved by experts to help the students to crack exercise very easily. These solutions help students to familiarize themselves with the data handling. Solutions are available in PDF format on BYJU’S website.

### List out the concepts covered in NCERT Solution for Class 8 Maths Chapter 5?

The concepts are covered in NCERT Solution for Class 8 Maths Chapter 5 are provided below

5.1 Looking for Information

5.2 Organising Data

5.3 Grouping Data

5.3.1 Bars with a difference

5.4 Circle Graph Or Pie Chart

5.4.1 Drawing pie charts

5.5 Chance and Probability

5.5.1 Getting a result

5.5.2 Equally likely outcomes

5.5.3 Linking chances to probability

5.5.4 Outcomes as events

5.5.5 Chances and Probability related to real life.

By learning these concepts students will be able to solve questions on Data handling.

## FAQs

### What is data handling for Class 8? ›

Mathematics NCERT Grade 8, Chapter 5: Data Handling- **The collection of any specific information is called data**. It is usually collected in the context of a situation that we want. Data in unorganised form is called raw data. For meaningful inferences, data must be organised systematically.

### What is the name of Chapter 5 of Class 8? ›

Class 8 English Chapter 5 | **The Summit Within** Full Chapter Explanation, Summary & NCERT Solutions - YouTube.

### What is data handling in maths 5? ›

Data handling means **collecting the set of data and presenting in a different form**. Data is a collection of numerical figures that represents a particular kind of information. The collection of observations which are gathered initially is called the raw data.

### What is data handling in maths class 8 introduction? ›

CBSE Class 8 Maths Notes Chapter 5 Data Handling. Data: **Numerical observations collected by an observer is called data (raw data)**. Frequency: The number of times an observation occurs in the given data is called the frequency of the observation.

### How do I make a pie chart in class 8? ›

Drawing pie Charts - Class 8 Maths (Meritnation.com) - YouTube

### What is a histogram class 8? ›

A histogram is **a graphical representation of a grouped frequency distribution with continuous classes**.

### What is raw data in maths class 8? ›

**A collection of observations gathered initially** is called raw data. or Data obtained from direct observation is called raw data. or Data mostly available to us in an unorganized form is called raw data. The marks obtained by 10 students in a monthly test are an example of raw data also known as ungrouped data.

### What is a coal Class 8? ›

Coal is **a fossil fuel and is a hard stone-like substance that is black in colour due to the high pressure and temperature it was buried under**. Coal is used as a heat source to cook food, to create steam to run trains and other engines, and in thermal power plants to generate electricity, among other things.

### What is simple equation? ›

What is Simple Equation? **A mathematical equation which represents the relationship of two expressions on either side of the sign**. It mostly has one variable and equal to symbol. Example: 2x – 4 = 2.

### What is raw data in Maths? ›

Raw data is defined as **a data that is not in form to be used or not yet processed**. The end product of data processing is known as information. Raw data is also called original data or primary data.

### What is a raw data? ›

Raw data (sometimes called source data, atomic data or primary data) is **data that has not been processed for use**. A distinction is sometimes made between data and information to the effect that information is the end product of data processing.

### What is pictograph Class 8? ›

A pictograph is **a pictorial representation of a word or expression**. It is one of the methods of recording data in a more interesting way. In pictograph, data is recorded in form of images and these images help us to understand statistical information in a much easier way.

### What is pictograph math? ›

The pictograph is **a method to represent the data using images**. Each image in the pictograph represents certain things. In other words, pictographs define the frequency of the data using images or symbols, which are relevant to the data.

### What is a report class 8? ›

A report is **a brief account of an event that has already taken place**. A report helps in recording events of importance that occurs in our day to day life. A report attempts to present the first hand information of an incident or event. A report of an event presents a record of events that took place.

### How do I change the color of my bar plot in Python? ›

How To Colorize The Bars In A Bar Graph In matplotlib - YouTube

### How do you plot a bar and line graph in Python? ›

**MatPlotLib with Python**

- Set the figure size and adjust the padding between and around the subplots.
- Make a two-dimensional, size-mutable, potentially heterogeneous tabular data.
- Create a figure and a set of subplots.
- Plot the bar and line with the dataframe obtained from Step 2.
- To display the figure, use show() method.

### How do I make a barplot in Python? ›

**How to Create a Bar Chart in Python using Matplotlib**

- Step 1: Install the Matplotlib package. ...
- Step 2: Gather the data for the bar chart. ...
- Step 3: Capture the data in Python. ...
- Step 4: Create the bar chart in Python using Matplotlib.

### Is pie a food? ›

The Concise Oxford English Dictionary (2008) defines pie simply as “**a baked dish of savory or sweet ingredients encased in or topped with pastry**.” The Oxford American Dictionary of Current English (1999) defines pie as “a baked dish of fruit, meat, custard, etc., usu.

### What is pie chart PDF? ›

The pie chart is **constructed by dividing a circle into two or more sections or slices**. The chart is used to show the proportion that each part is of the whole. Hence, it should be used when you want to compare individual categories with the whole.

### What is the formula for pie chart? ›

Reading Pie Charts

To calculate the percentage each slice is worth, **measure the angle of each slice and divide this by 360 then multiply it by 100** . To find the number of pieces of data each slice represents, multiply the percentage that each slice is worth by the total number of the data sets.

### What is a pie chart in math? ›

A pie chart is **a type of graph that represents the data in the circular graph**. The slices of pie show the relative size of the data, and it is a type of pictorial representation of data. A pie chart requires a list of categorical variables and numerical variables.

### What is a bar graph in math? ›

Bar Charts and Bar Graphs Explained - YouTube

### What is ogive curve? ›

The Ogive is defined as **the frequency distribution graph of a series**. The Ogive is a graph of a cumulative distribution, which explains data values on the horizontal plane axis and either the cumulative relative frequencies, the cumulative frequencies or cumulative per cent frequencies on the vertical axis.

### What is a math array? ›

**An arrangement of objects, pictures, or numbers in rows and columns** is called an array. Arrays are useful representations of multiplication concepts (among other ideas in mathematics).

### Why is data so important? ›

Good data **allows organizations to establish baselines, benchmarks, and goals to keep moving forward**. Because data allows you to measure, you will be able to establish baselines, find benchmarks and set performance goals. A baseline is what a certain area looks like before a particular solution is implemented.

### How do u find the mean? ›

How to Calculate the Mean - YouTube

### Why is petroleum called black gold? ›

Petroleum is also known as Black Gold - **because when crude oil is extracted from the land it is black in color**. People call it gold because of its oils and value . It is very difficult to find.

### Why is coal known as black gold? ›

It is called black gold simply **due to its commercial value**. Coal is also black and a common source of fuel but the term 'black gold' is not used for coal, it is used for petroleum.

### Is kerosene a fossil fuel? ›

Petrol, diesel and kerosene are products that are obtained by refining petroleum. Hence, **kerosene is also a fossil fuel**.

### What do you mean by data handling? ›

Data handling is **the process of ensuring that research data is stored, archived or disposed off in a safe and secure manner during and after the conclusion of a research project**. This includes the development of policies and procedures to manage data handled electronically as well as through non-electronic means .

### What is data handling with examples? ›

Examples of data handling

**Taking stock of the remaining buns after a school bake sale**. Creating a tally chart of what colour eyes class-mates have. Drawing a pie chart to show how many boys and girls there are in a class. Making a bar chart to show different people's favourite colours.

### What is data handling and its types? ›

The two types of data handling are qualitative data and quantitative data. Quantitive data gives numerical information, while qualitative data gives descriptive information about anything. Quantitative can be either discrete or continuous data.

### What is data handling in maths class 7? ›

**For data to be meaningful and useful the items of data must be gathered or captured and recorded in a systematic manner**. This is referred to as data handling. Data handling may be as simple as orderly recording on a sheet of paper or the completion of entry forms on a computer screen.

### What are different types of data? ›

4 Types of Data: **Nominal, Ordinal, Discrete, Continuous**.

### What is a raw data? ›

Raw data (sometimes called source data, atomic data or primary data) is **data that has not been processed for use**. A distinction is sometimes made between data and information to the effect that information is the end product of data processing.

### What are the 4 stages of data processing? ›

It is usually performed in a step-by-step process by a team of data scientists and data engineers in an organization. The raw data is **collected, filtered, sorted, processed, analyzed, stored**, and then presented in a readable format.

### What is a line graph in math? ›

What is a Line Graph? A line graph, also known as a line chart or a line plot, is **commonly drawn to show information that changes over time**. You can plot it by using several points linked by straight lines. It comprises two axes called the “x-axis” and the “y-axis”. The horizontal axis is called the x-axis.

### How do u find the mean? ›

How to Calculate the Mean - YouTube

### What is the mean in data? ›

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

### How is data handling used in real life give 4 examples? ›

Data handling is used for organizing ur data properly

1)**In libraries -To keep a record of books**. 5)For recording water levels in rivers. 6)For recording the economical income of each household.

### What is pictograph math? ›

The pictograph is **a method to represent the data using images**. Each image in the pictograph represents certain things. In other words, pictographs define the frequency of the data using images or symbols, which are relevant to the data.

### What is graph in data handling? ›

The numerical data is represented through pictures or diagrams then it is called pictorial representation of data. **The pictorial or visual representation for easy understanding a given data** is called graph.

### How do you choose a 7th scale? ›

(a) We will choose a scale as **1 unit = 10 children** because we can represent a more clear difference between the number of students of class 7^{th} and that of class 9^{th} by this scale. (i) Since the bar representing the number of children for class fifth is the tallest, there are maximum number of children in class fifth.

### What is a mode math? ›

How to Find the Mode | Math with Mr. J - YouTube

### What is mean class 7th? ›

Mean is **the average of the given numbers** and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations)