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Data Handling and Presentation: questions with answers

Class 6 Maths, Chapter 4 (NCERT). 15 questions by concept, 15 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Accurate and Appealing Data Displays

Question 1

The figure shows an infographic where the printed numbers are correct. Which feature could still mislead a reader?

Intended Comparison: lengthSmall: 2Medium: 4Large: 6?
  1. (a)No feature is misleading because attractive pictures make the infographic easier to enjoy.
  2. (b)The title is the problem, even though it correctly names the data shown by length.
  3. (c)The colours are the problem because brighter colours must mean larger length values.
  4. (d)The larger data icons are larger in total area, so readers may compare decorative size instead of length.
Show answer

(d) The larger data icons are larger in total area, so readers may compare decorative size instead of length.

Correct numbers are not enough if the visual design suggests extra information. When a larger value is shown by an icon that is both larger in total area, readers may compare area instead of the intended length.

Data and Data Collection

Question 2

What is needed to answer the question shown for the locality?

our localitywater wasted in our locality this month: ??
  1. (a)Use an atlas because our locality is a named place.
  2. (b)Collect current data in our locality for this month.
  3. (c)Ask classmates even if they have not observed the locality.
  4. (d)Use a fixed fact from memory because water wasted never changes.
Show answer

(b) Collect current data in our locality for this month.

The question is about a quantity in a particular locality during a current time period. It cannot be answered as a stable known fact; data must be collected from that place and time.

Question 3

What is the best method for answering the question shown on the classroom board?

Which fruit is mostpopular in our section?Tally?
  1. (a)Collect data from our section using a survey or tally.
  2. (b)Ask only one friend and treat that as the answer for our section.
  3. (c)Use memory or a textbook because the most popular fruit is a fixed fact.
  4. (d)Guess one fruit without collecting evidence.
Show answer

(a) Collect data from our section using a survey or tally.

The board asks which fruit is most popular in our section. This is a current preference of the students, not a fixed fact. So the suitable method is to collect data from our section, such as by a survey or tally.

Tally Marks and Frequency Tables

Question 4

Use the figure. Which classification of questions is correct for this frequency table?

Activity choicesActivityNumber of studentsFootball3Kho-kho5Chess4How many chose Kho-kho? ?Which activity did Meena choose? ?Do more chose Kho-kho than Chess? ?
  1. (a)Answerable from the table: every question about counts and named student choices. Not answerable from the table: none of these questions.
  2. (b)Answerable from the table: How many students chose Kho-kho? Not answerable from the table: Do more students choose Kho-kho than Chess?
  3. (c)Answerable from the table: How many students chose Kho-kho? Not answerable from the table: Which activity did Meena choose?
  4. (d)Answerable from the table: Which activity did Meena choose? Not answerable from the table: How many students chose Kho-kho?
Show answer

(c) Answerable from the table: How many students chose Kho-kho? Not answerable from the table: Which activity did Meena choose?

A frequency table can answer questions about category counts, totals, and comparisons of counts. It cannot answer which category a particular named student chose unless the original individual choices or grouped names are also given.

Question 5

Use the figure. Six students are to receive the fruit they chose, but only the frequency table was kept. What extra information is needed to give the correct fruit to each student?

Fruit choicesFruitNumber of studentsMangoGuavaApple132StudentsRiyaOmarLeelaKabirNitaSam??????
  1. (a)Only the total number of students, 6.
  2. (b)Only the category names: Mango, Guava, Apple.
  3. (c)No extra information is needed; use the frequencies to give out the fruits.
  4. (d)Which fruit each named student chose, or the names written under each fruit.
Show answer

(d) Which fruit each named student chose, or the names written under each fruit.

The table gives only the number of students for each fruit. It does not tell which fruit each named student chose. To give out the fruits correctly, we need each student's choice, or the names written under each fruit.

Question 6

The frequency table shown gives the number of stickers in a packet and how many packets have that many stickers. Which expression gives the total number of stickers?

Stickers in a packetFrequency335581expression for total = ?
  1. (a)(3 + 5 + 8) × (3 + 5 + 1)
  2. (b)3 + 5 + 1
  3. (c)3 + 5 + 8
  4. (d)3 × 3 + 5 × 5 + 8 × 1
Show answer

(d) 3 × 3 + 5 × 5 + 8 × 1

The frequency tells how many packets have each number of stickers. So multiply each packet size by its frequency and then add. The correct expression is 3 × 3 + 5 × 5 + 8 × 1.

Pictographs and Scale

Question 7

Use the pictograph to choose the correct statement about its key.

PictographKey1 ball= 50 ballsGames balls
  1. (a)The key is only decoration and is not needed to read the pictograph.
  2. (b)The category label "Games balls" is the key.
  3. (c)Each picture stands for 50 balls.
  4. (d)Each picture stands for 1 ball.
Show answer

(c) Each picture stands for 50 balls.

The key tells how many real objects one picture represents. Here, each ball picture stands for 50 balls, so the pictures must be read using that scale.

Question 8

Use the pictograph. One full circle symbol represents 20 children and one half circle symbol represents 10 children. How many more children chose Mango than Apple?

1 full circle = 20 children1 half circle = 10 childrenMangoAppleDifference = ? children
  1. (a)60 children
  2. (b)40 children
  3. (c)2 children
  4. (d)50 children
Show answer

(d) 50 children

Mango represents 100 children and Apple represents 50 children. The difference is 100 - 50 = 50 children.

Question 9

Use the pictograph. One full book symbol represents 100 students. How many students like subjects other than English and Mathematics?

1 book = 100 studentsHindiEnglishMathematicsScienceSocial StudiesExcludedExcludedOther subjects = ? students
  1. (a)500 students
  2. (b)1300 students
  3. (c)13 students
  4. (d)1500 students
Show answer

(b) 1300 students

Find the total represented by all subjects except English and Mathematics. The included subjects are Hindi, Science, and Social Studies, so the required number is 400 + 500 + 400 = 1300 students.

Bar Graphs and Scale

Question 10

The figure shows a bar graph of the books read by A, B and C. Is the scale on its vertical axis correctly started, and why?

Books readNumber of books ?10203040ABC
  1. (a)No, because the first number marked on the vertical axis is not 0.
  2. (b)Yes, because the gaps between the numbers on the vertical axis are equal.
  3. (c)No, because the numbers on the vertical axis go up by 10, not by 1.
  4. (d)Yes, because every bar starts from the horizontal axis.
Show answer

(a) No, because the first number marked on the vertical axis is not 0.

The markings on the vertical axis must start from 0. Here the first number marked is 10, so the scale is not correctly started. A scale may go up in steps of 10, and equal gaps alone do not show where it starts.

Question 11

The figure shows a table of categories and their values. A bar graph is to be drawn from this table. How many bars are needed?

Categories: A, B, C, D, ECategoryValueABCDE2020202020Total100ValueCategory?
  1. (a)5
  2. (b)1
  3. (c)10
  4. (d)6
Show answer

(a) 5

A bar graph needs one bar for each category. Repeated values are not combined, and the Total row is not a category. The required number of bars is 5.

Question 12

The graph compares the number of tickets for different categories. By how many tickets is Delhi more than Jaipur?

01234567891011AgraKochiJaipurDelhiUnit lengths1 unit length = 10 tickets?
  1. (a)5 tickets
  2. (b)100 tickets
  3. (c)50 tickets
  4. (d)150 tickets
Show answer

(c) 50 tickets

Use the scale 1 unit length = 10 tickets to read the two bars. Delhi has 100 tickets and Jaipur has 50 tickets. The difference is 100 - 50 = 50 tickets.

Drawing Bar Graphs from Tables

Question 13

Use the data and proposed scales in the figure. Which statement is correct about Scale A?

Books readClass VI: 25 booksClass VII: 40 booksClass VIII: 60 booksScale A: 1 unit = 5 books ?Scale B: 1 unit = 10 books10 unit spaces
  1. (a)Scale A is suitable because the first value needs only 5 unit spaces.
  2. (b)Scale A is suitable because Scale A: 1 unit = 5 books uses a smaller number than Scale B: 1 unit = 10 books.
  3. (c)Scale A is unsuitable because the largest value would need 12 unit spaces, but the axis has only 10 unit spaces.
  4. (d)Scale A is unsuitable because it is not 1 unit = 1 book.
Show answer

(c) Scale A is unsuitable because the largest value would need 12 unit spaces, but the axis has only 10 unit spaces.

Scale A is checked against the largest value, not just the first value. The largest value is 60 books. With Scale A, required height = 60 / 5 = 12 unit spaces, which is more than the 10 unit spaces available. So Scale A is unsuitable.

Question 14

The figure shows a graph started with an old scale, but the largest table value would go past the fixed top of the axis. Which fix corrects the graph without changing the table values or the axis length?

160 students8 unit spaces1 unit = 20 studentsSports Club: 200 studentsCorrected scale: 1 unit = ? students
  1. (a)Keep 1 unit = 20 students and extend the axis to 10 unit spaces.
  2. (b)Change the largest table value to 160 students and keep the old scale.
  3. (c)Keep 1 unit = 20 students and let the largest bar go past the top.
  4. (d)Change the scale to 1 unit = 40 students.
Show answer

(d) Change the scale to 1 unit = 40 students.

The table values must stay the same, and the axis still has 8 unit spaces. With the old scale, the largest value would need 10 unit spaces, so it does not fit. With 1 unit = 40 students, the largest bar height is 5 unit spaces, so it fits.

Question 15

Use the table and the blank vertical axis in the figure. Which scale should be written where it says 1 unit = ? so that all bars fit in the available unit spaces and the bar heights are convenient?

Items collectedCategoryItemsPens:30 itemsPencils:50 itemsCrayons:80 itemsErasers:60 items8 unit spaces1 unit = ? items
  1. (a)1 unit = 30 items
  2. (b)1 unit = 10 items
  3. (c)1 unit = 1 item
  4. (d)1 unit = 12 items
Show answer

(b) 1 unit = 10 items

The maximum value is 80 items and the axis has 8 unit spaces. With 1 unit = 10 items, the maximum bar is 8 unit spaces, so it fits. The other bar heights are 3, 5, 6, and 8 unit spaces, which are convenient to draw.

Common misconception in Data Handling and Presentation

Open full misconception guide →

What does one picture stand for?

Wrong

Five symbols mean five books.

Why it feels right. Each picture looks like a single book.

Right

Read the pictograph key before counting.

Worked example

Key
📘4 books
Pictograph
📘
📘
📘
📘
📘
Actual count
4
4
4
4
4
Five book symbols each stand for four books, giving 20 books.
  1. The key says one symbol stands for 4 books.
  2. Five symbols represent 5 × 4 = 20 books.