Data Handling and Presentation Class 6 (Ganita Prakash)

Master Data Handling and Presentation Class 6 (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.

NCERT Solutions

Data Handling and Presentation Class 6 (Ganita Prakash) – NCERT Solutions

Each question below opens its complete step-by-step Teachoo solution.

Figure it out (Page 77 to 79)

6 questions

Question 1 (Page 77-79)

Help her to figure out the following: a. The largest shoe size in the class is _________. b. The smallest shoe size in the class is _________. c. There are _________ students who wear shoe size 5. d. There are _________ students who wear shoe sizes larger than 4.This is our data

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Question 2 (Page 77-79)

How did arranging the data in ascending order help to answer these questions?Arranging the data in ascending order helped significantly because:
It made it very easy to find the smallest and largest shoe sizes by simply looking at the first and last numbers in the list.
It grouped all the same shoe sizes together, which made counting how many students wear a specific size (like size 5) much faster and more accurate than searching through the jumbled grid.

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Question 3 (Page 77-79)

ArYes,
Another common way to arrange this data would be to create a frequency distribution table using tally marks.
This would show each shoe size and exactly how many students wear it.
You could also arrange the data in descending order (from largest to smallest).

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Question 4 (Page 77-79)

Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table: a. Which tree was found in the greatest number? b. Which tree was found in the smallest number? c. Were there any two trees found in the same numbers?Let’s try to complete our table

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Question 5 (Page 77-79)

Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters ‘c’, ‘e’, ‘i’, ‘r’, and ‘x’ in the words of the news article, and fill in the table. (a) The letter found the most number of times is ________. (b) The letter found the least number of times is ________. (c) List the five letters ‘c’, ‘e’, ‘i’, ‘r’, ‘x’ in ascending order of frequency. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order ‘x, c, r, i, e’.) Why do you think this is the case?(d) Write the process you followed to complete this task. (e) Discuss with your friends the processes they followed. (f) If you do this task with another news item, what process would you follow?Alright, let’s first complete our table – then answer questions one by one

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Figure it out (Page 93-100)

11 questions

Question 1

Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected: Help her prepare a bar graph representing this data.Here
We use numbers in y-axis, so Number of insects are in y-axis
And Insect names are in x-axis
Since numbers are from 2 to 10, we take
Scale 1 unit length = 1 number

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Question 2

Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a two-hour period. She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.(a) Write the number of tickets sold for Vidisha above the bar. (b) Write the number of tickets sold for Jabalpur above the bar. (c) The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph? (d) Draw the correct bar for Sagar. (e) Add the scale of the bar graph by placing the correct numbers on the vertical axis. (f) Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).Alright, to answer this, we first
Label the bar graph properly
Identify scale of the bar graph
Add bar for Sagar and complete the bar graph
Let’s follow these steps
Since Vidisha has 24 tickets, and there are 6 horizontal lines
So, 1 line is 24/6 = 4 tickets
And, scale is 1 unit = 4 tickets
Now, we see that
Bar for Indore is wrong, so let’s change that
Adding Bar for Sagar

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Question 3

Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.: (a) Prepare a frequency distribution table for the data. (b) Which means of transport was used the most? (c) If you were there to collect this data, how could you do it? Write the steps or process.Let’s answer our questions
Prepare a frequency distribution table for the data.
Its made above
(b) Which means of transport was used the most?
Bike was used the most (13)
(c) If you were there to collect this data, how could you do it? Write the steps or process.
We follow these steps
Stand in a safe place with a view of the road.
Create a table with the names of different types of transport.
For each vehicle that passes, make a tally mark in the correct row.
After the time period is over (e.g., one hour), count the tally marks to get the frequency.

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Question 4

Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared: (a) The minimum number of times. (b) The maximum number of times. (c) Find numbers that appeared an equal number of times.Let’s actually try to do this and make some raw data like this

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Question 5

(a) Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: (a) What information is this table giving? The table shows how many matches Jaspreet Bumrah played where he took a certain number of wickets, over his last 30 matches.
Question 5 (b) (b) What may be the title of this table? "Number of Wickets Taken by Jaspreet Bumrah in his Last 30 Matches"
Question 5 (c) (c) What caught your attention in this table? Answers will vary, but one might notice that the most frequent outcome was taking 3 wickets in a match – which is very consistent
Question 5 (d) (d) In how many matches has Bumrah taken 4 wickets?In 3 matches, Bumrah has taken 4 wickets
Question 5 (e) (e) Mayank says, “If we want to know the total number of wickets he has taken in his last 30 matches, we have to add the numbers 0, 1, 2, 3 …, up to 7.” Can Mayank get the total number of wickets taken in this way? Why?No, Mayank is incorrect. This method only sums the categories, not the total wickets.
Question 5 (f) (f) How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?We need to multiply the wickets taken by the number of matches for each row and then add them all together:

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Question 6

The following pictograph shows the number of tractors in five different villages. (c) How many more tractors does Village C have than Village B? (d) Komal says, “Village D has half the number of tractors as Village E.” Is she right? Observe the pictograph and answer the following questions - (a) Which village has the smallest number of tractors? (b) Which village has the most tractors? Writing pictograph it in table

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Question 7

The number of girl students in each class of a school is depicted by the pictograph: Writing it in table
Let’s answer our questions

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Question 8

Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka’s Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows — Village A : 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F : 24 Prepare a pictograph and answer the following questions: (a) What will be a useful scale or key to draw this pictograph? (b) How many symbols will you use to represent the dogs in Village B? (c) Kamini said that the number of these dogs in Village B and Village D together will be more than the number of these dogs in the other 4 villages. Is she right? Give reasons for your response. Now to make Pictograph, we need a scale
Our data is
Village A : 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F : 24

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Question 9

A survey of 120 school students was conducted to find out which activity they preferred to do in their free time: Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?Here number of students are from 10 to 45
And given that, scale is 1 unit length = 5 students

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Question 10

Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows — (a) The total number of saplings planted on Wednesday and Thursday is
70 (30 + 40)
(b) The total number of saplings planted during the whole week is
280 (50 + 40 + 30 + 40 + 50 + 60 + 40).
(c) The greatest number of saplings were planted on _____ and the least number of saplings were planted on _____ . Why do you think that is the case? Why were more saplings planted on certain days of the week and less on others? Can you think of possible explanations or reasons? How could you try and figure out whether your explanations are correct?

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Question 11

The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in four year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them? Fixing the graph
The mistakes in the bar graph are:
The bar for 2006 is too short. It should represent 1400
The bar for 2010 is short – it looks like 1500, but it should be increased to 1700
The bar for 2014 is too long – it looks like 2900, but it should be decreased to 2200
The bar for 2018 is too short – it looks like 2200, but it should be increased to 1700
The bar for 2022 appears to be correct.

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Why Learn This With Teachoo?

Learn Data Handling and Presentation Class 6 with clear notes on collecting data, tally marks, pictographs, bar graphs and infographics, together with Ganita Prakash solutions and practice resources on Teachoo.

Data Handling and Presentation is Chapter 4 of the current NCERT Ganita Prakash Class 6 Mathematics book. It explains how raw information is collected, organised, displayed and interpreted.

Data surrounds us: attendance figures, temperatures, survey responses, scores, prices and travel times are all data. A long unorganised list is difficult to understand. When the same information is placed in a table, pictograph or bar graph, patterns become visible and comparisons become easier.

What Is Data?

Data is a collection of facts, numbers, measurements, observations or descriptions that provide information. Students learn that data can come from counting, measuring, observing or asking questions.

The chapter distinguishes between raw data and organised data. Raw data is information in the form in which it was first collected. Organised data is grouped or arranged so that it can be read and interpreted more easily.

Collecting and Organising Data

Students learn to begin with a clear question. For example: “Which sport is most popular in the class?” They then decide whom to ask, record each response and arrange the results into categories.

Good data handling requires accuracy. If responses are missed, counted twice or placed in the wrong group, every graph made from that data will be misleading.

Tally Marks

Tally marks provide a fast way to record frequencies. The first four observations are shown using vertical marks, and the fifth crosses the group. This grouping in fives makes counting faster and reduces errors.

Students use tally marks to create frequency tables and answer questions such as which category occurs most often, least often or how much one category exceeds another.

Pictographs

A pictograph represents data using pictures or symbols. A key explains the numerical value of one symbol. For example, one book symbol may represent five books.

Students learn to:

  • Read the key before interpreting the pictograph.

  • Multiply the number of symbols by the value of each symbol.

  • Interpret partial symbols when allowed by the key.

  • Select a scale that avoids an unnecessarily large number of pictures.

  • Draw a neat pictograph with labels and equal-sized symbols.

Bar Graphs

A bar graph displays categories using rectangular bars of equal width. The length or height of each bar represents its value.

A complete bar graph should contain:

  • A clear title

  • Labelled horizontal and vertical axes

  • An appropriate scale

  • Equal-width bars

  • Equal gaps between bars

  • Accurate bar heights

Teachoo explains both reading and drawing bar graphs. Students learn to compare categories, find differences and make statements supported by the data.

Artistic and Aesthetic Considerations

A data display must be accurate, but it should also be readable. Colour, spacing, scale and labels should help the reader rather than distract them. A visually attractive graph is not useful if its scale is misleading or its labels are missing.

Infographics

Infographics combine numbers, short text and visual elements to communicate information quickly. Students learn to distinguish a useful infographic from a decorative image and to check whether its visual comparisons honestly represent the data.

NCERT Questions and Resources

Teachoo’s page covers the chapter concept-wise and includes Ganita Prakash “Figure it Out” question sets from pages 77–79 and 93–100. It also provides separate explanations for tally marks, pictographs, drawing pictographs, bar graphs, drawing bar graphs, infographics and representing data.

What Students Should Be Able to Do

After completing the chapter, students should be able to:

  • Define data and give examples.

  • Collect information for a specific question.

  • Organise raw data into categories.

  • Record frequencies using tally marks.

  • Read and draw pictographs using a key.

  • Read and draw bar graphs using a suitable scale.

  • Compare categories and make valid inferences.

  • Identify misleading or unclear presentations.

  • Choose an appropriate representation for a dataset.

How to Study Data Handling

Create a small survey of your own. Collect responses from family members or classmates, prepare a tally table and display the same data as a pictograph and bar graph. Then write three conclusions that can be verified from the display.

This active exercise is more useful than memorising definitions because it connects the complete data cycle: question, collection, organisation, representation and interpretation.

Common Mistakes in Data Representation

Students often forget the key in a pictograph, use unequal gaps between bars or choose a scale that does not fit the data. Another mistake is drawing bars with different widths, which makes the comparison visually unreliable. When interpreting a graph, do not make a claim that the display cannot support. A class survey can show which option was most popular among those surveyed; it cannot automatically prove what every student in the city prefers. Always separate the observed data from a broader conclusion.

Deeper reasoning and concept connections

Study Data Handling and Presentation through comparison and justification. Place two related examples side by side, identify the decisive difference and explain why one method works in each case. Then create a new example and a deliberate non-example. This forces the definition to do real work and exposes gaps that passive reading hides.

Students should also practise reversing questions. After solving for an answer, ask what question could have produced it, whether more than one answer is possible and which extra condition would make the result unique. Reverse reasoning develops flexibility and is especially useful for missing-value, assertion–reason and error-analysis questions. The goal is to understand the network of ideas, not merely the order of a textbook solution.

How to solve unfamiliar and competency-based questions

Begin by separating facts from conclusions. Facts are given by the question or a known property; conclusions must be derived. Draw or rewrite the problem so each fact has a visible place. If several methods are possible, prefer the one with fewer assumptions and an easy final check. Record intermediate results rather than doing everything mentally.

Competency questions often change context without changing mathematics. Replace names and story details with variables, shapes, sets or data values. After solving, restore the context and check feasibility: counts should be whole where required, lengths and areas should have suitable units, probabilities should lie between 0 and 1, and constructed figures should satisfy every stated condition.

What complete mastery looks like

For Data Handling and Presentation, a student should be able to define the central ideas in simple language, recognise them in different representations, solve routine questions accurately and explain the method used. They should also be able to correct a flawed solution, create an example satisfying given conditions and combine two ideas from the chapter in one problem. A reliable mastery test is to solve one direct question, one application question and one reasoning question without looking at notes, then explain all three aloud or in writing.

Keep a compact error log with four labels: concept, interpretation, calculation and presentation. Reattempt each error after a gap instead of rereading the answer immediately. Improvement comes from correcting the decision that caused the mistake, not from repeating questions whose method is already known.

Additional frequently asked questions

What should a student know before starting Data Handling and Presentation?

Revise the definitions, number operations, diagrams or notation used at the beginning of the chapter. The prerequisite list should be short: if an earlier skill blocks progress, repair that skill with two or three focused questions and return to the chapter.

How can a student check an answer in Data Handling and Presentation?

Use an independent check whenever possible: substitute the result, reverse the operation, estimate its size, compare it with the figure, test a simpler case or solve using another representation. A check should examine the mathematical condition, not merely repeat the same arithmetic.

How many questions are enough for strong preparation?

There is no fixed number. Stop counting questions and track coverage: every concept, every standard method, at least one mixed problem, one competency-based problem and every previously incorrect type should be solved independently. Ten varied, analysed questions are more valuable than fifty copied solutions.

How should Teachoo solutions be used without becoming dependent on them?

Attempt the question first and mark the exact step where progress stops. Read only enough of the solution to repair that step, close it and restart the question. Finally, solve a similar problem without help. This turns a solution into feedback rather than a substitute for thinking.

Frequently Asked Questions

What is data handling in Class 6?

Data handling is the process of collecting, organising, representing and interpreting information.

What representations are taught in Ganita Prakash Chapter 4?

The chapter covers tally tables, pictographs, bar graphs and infographics.

What is the most common mistake in a pictograph?

Students often count the symbols but forget to multiply by the value stated in the key.

Does Teachoo provide Chapter 4 NCERT solutions?

Teachoo provides concept-wise explanations and solutions to the listed Ganita Prakash “Figure it Out” questions.

Open a topic, read the scale or key carefully and support every conclusion with the actual data shown.