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Data Handling

NCERT Class 5 · Mathematics Based on NCERT Class 5 Mathematics textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter introduces students to the concept of data handling, which is the process of collecting, recording, and representing information in an organized way. It exists in the syllabus to build foundational skills in interpreting and creating visual data representations like pictographs and bar graphs. The one big idea a student must walk away with is that data can be collected from everyday life, organized using tables, and shown through pictures or bars to make comparisons and answer questions easily.
Key Concepts (10)
Data
Information collected in the form of numbers or facts about a specific topic.
e.g. Samaira and Kabir asked 35 friends how many hours a day they spend watching TV and wrote down their answers.
Pictograph
A way of representing data using pictures or symbols, where each picture stands for a certain number of items.
e.g. Joseph Uncle used one picture of a toy to represent 5 toys in his shop.
Scale
A key or rule that tells us how many items one picture or symbol represents in a pictograph.
e.g. In Dipesh's pictograph, the scale was: one icon = 5 toys, one icon = 5 board games, one icon = 5 sports items.
Bar Graph
A chart that uses vertical or horizontal bars of different lengths to show and compare data.
e.g. Sheela recorded her daily routine by drawing vertical bars for each activity, with the height of the bar showing the number of hours.
Horizontal Base
The bottom line of a bar graph on which the names of different activities or items are written.
e.g. In Sheela's bar graph, the horizontal base showed activities like Sleeping, Time in school, Studying, Eating and playing, and Other activities.
Vertical Line
The side line of a bar graph that shows the number or quantity, usually marked with numbers.
e.g. In Sheela's bar graph, the vertical line showed the number of hours from 0 to 10.
Icon
A small picture or symbol used in a pictograph to represent a fixed number of items.
e.g. Deepti used one icon of a two-wheeler to show 3 two-wheelers passing her house.
Table
An organized way of writing data in rows and columns for easy reading.
e.g. Raman recorded his daily routine in a table with two columns: Activities and Number of Hours.
Food Wastage
The amount of food that is thrown away or not eaten, measured in kilograms.
e.g. Rani's school dining hall displayed a bar graph showing how much food was wasted each day for different items like sandwich, paratha, khichdi, puri-sabzi, and idli-sambar.
True or False Statements
Statements based on observation of a picture or graph that must be judged as correct or incorrect.
e.g. From a picture of children, statements like 'All girls are wearing glasses' or '10 children are wearing caps on their heads' were marked true or false.
Formulas & Equations (3)
Total items = Number of icons × Value of each icon
Reads as: Total items equals number of icons multiplied by the value each icon represents.
Variables: Number of icons = count of pictures used; Value of each icon = the number each picture stands for (e.g., 5 toys per icon).
Use when: When calculating the actual number of items from a pictograph with a given scale.
⚠ Students forget to multiply by the scale and just count the icons as one each.
Number of icons needed = Total items ÷ Value of each icon
Reads as: Number of icons needed equals total items divided by the value each icon represents.
Variables: Total items = actual count of objects; Value of each icon = the number each picture stands for.
Use when: When creating a pictograph and deciding how many icons to draw for a given quantity.
⚠ Students divide incorrectly or forget to round up when there is a remainder.
Number of children fed = Total food wasted (kg) × Number of children per kg
Reads as: Number of children fed equals total food wasted in kilograms multiplied by the number of children one kilogram can feed.
Variables: Total food wasted = sum of all food wasted in kg; Number of children per kg = given constant (e.g., 3 children per kg).
Use when: When calculating how many children could be fed with the wasted food, as in the food wastage problem.
⚠ Students divide instead of multiply, or forget to add all food wastage first.
How It Works
Collecting Data
  1. Step 1: Decide what information you want to collect (e.g., hours spent watching TV).
  2. Step 2: Ask a group of people (e.g., 35 friends) and write down their answers.
  3. Step 3: Organize the answers in a notebook or table for easy reading.
💡 Data must be collected from real people or observations, not made up.
Making a Pictograph
  1. Step 1: Count the total number of items for each category (e.g., toys, board games, sports items).
  2. Step 2: Choose a scale (e.g., one icon = 5 items) so that you don't have to draw too many pictures.
  3. Step 3: Draw the correct number of icons for each category based on the scale.
  4. Step 4: Write the scale clearly so anyone reading the pictograph understands what one icon means.
💡 The scale must be consistent for all categories in the same pictograph.
Reading a Pictograph
  1. Step 1: Look at the scale to know what one icon represents.
  2. Step 2: Count the number of icons for the category you are interested in.
  3. Step 3: Multiply the number of icons by the scale value to get the actual number.
  4. Step 4: Compare different categories by looking at the number of icons.
💡 Always check the scale first — never assume one icon equals one item.
Making a Bar Graph
  1. Step 1: Draw a horizontal base line and write the names of activities or items on it.
  2. Step 2: Draw a vertical line on the left side and mark numbers (e.g., 0 to 10) for the quantity.
  3. Step 3: For each activity, draw a bar whose height matches the number from the data.
  4. Step 4: Make sure all bars have the same width and are evenly spaced.
💡 The height of the bar must exactly match the number it represents — no gaps or extra space.
Reading a Bar Graph
  1. Step 1: Look at the labels on the horizontal base to know what each bar represents.
  2. Step 2: Look at the numbers on the vertical line to understand the scale.
  3. Step 3: Read the height of each bar to find the value for that category.
  4. Step 4: Compare bars by their heights to answer questions like 'which is more' or 'how many more'.
💡 Always read the vertical scale carefully — sometimes one small division may represent more than one unit.
Determining True or False from a Picture
  1. Step 1: Observe the picture carefully and count the number of children or objects with each feature (e.g., glasses, caps, books).
  2. Step 2: Read each statement one by one.
  3. Step 3: Compare the statement with your observation.
  4. Step 4: Mark 'True' if the statement matches the observation, otherwise mark 'False'.
💡 Count accurately — a single mistake in counting can make the whole answer wrong.
Exam Traps — Don't Make These Mistakes
⚠ Forgetting the Scale in a Pictograph
✗ Joseph Uncle has 3 toys (because they see 3 icons).
→ The student ignored the scale that says one icon = 5 toys. They counted icons instead of multiplying by the scale.
✓ Joseph Uncle has 3 icons × 5 toys per icon = 15 toys.
⚠ Misreading the Bar Graph Vertical Scale
✗ The food wasted on Monday is 9 kg (because the bar touches the line near 9).
→ The student did not check that the vertical scale goes up in ones and the bar actually ends at 8 kg.
✓ The food wasted on Monday is 8 kg (read the exact number where the bar ends on the vertical axis).
⚠ Adding Instead of Subtracting for 'How Many Fewer'
✗ There were 12 fewer two-wheelers on Wednesday than on Monday (adding 6 and 6).
→ The student added the numbers instead of subtracting the smaller from the larger. 'Fewer' means difference, not total.
✓ Monday had 6 icons × 3 = 18 two-wheelers. Wednesday had 4 icons × 3 = 12 two-wheelers. Difference = 18 − 12 = 6 fewer two-wheelers on Wednesday.
⚠ Confusing 'More Than' and 'Less Than' in Time Data
✗ More children watch TV for two hours than half an hour. (Answer: False)
→ The student guessed without counting. The table shows 8 children watch for half an hour and 10 children watch for two hours, so the statement is actually True.
✓ Count carefully: half an hour = 8 children, two hours = 10 children. Since 10 > 8, the statement is True.
⚠ Not Rounding Up When Drawing Icons
✗ For 17 toys with scale 1 icon = 5 toys, draw 3 icons (because 17 ÷ 5 = 3.4, and they round down).
→ 3 icons represent only 15 toys, leaving 2 toys unrepresented. In pictographs, you must draw a partial icon or round up to show the full count.
✓ Draw 3 full icons (15 toys) and one partial icon to represent the remaining 2 toys, or choose a different scale.
Compare & Contrast
Method of representing data
Pictograph
Bar Graph
A pictograph uses pictures or icons to show data, while a bar graph uses vertical or horizontal bars of different heights.
Format of data presentation
Raman's Recording (Table)
Sheela's Recording (Bar Graph)
Raman recorded his daily routine in a table with rows and columns, while Sheela recorded the same type of data using a vertical bar graph with a horizontal base and vertical line showing hours.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 Short Answer (3 marks) on reading a pictograph or bar graph, 1 Long Answer (5 marks) on creating a pictograph or bar graph from given data and answering questions.
Most asked: Reading and interpreting pictographs with a given scale · Reading and interpreting bar graphs · Calculating total items from a pictograph using multiplication · Answering 'how many more' or 'how many fewer' questions from graphs · Choosing an appropriate scale for a pictograph
Don't skip: Creating a pictograph or bar graph from a given data table and answering follow-up questions (5 marks); Interpreting a bar graph to find totals, differences, and comparisons (3 marks)
One-Line Revision (read aloud before the exam)
  1. Data is information collected from people or observations, like asking friends how many hours they watch TV.
  2. A pictograph uses pictures or icons to represent data, and each icon stands for a fixed number called the scale.
  3. The scale in a pictograph tells you how many items one picture represents, e.g., one icon = 5 toys.
  4. To find the actual number from a pictograph, multiply the number of icons by the scale value.
  5. A bar graph uses bars of different heights to show and compare data easily.
  6. In a bar graph, the horizontal base lists the categories, and the vertical line shows the numbers.
  7. To read a bar graph, look at the height of each bar and match it to the number on the vertical axis.
  8. When comparing two quantities, subtract the smaller from the larger to find 'how many more' or 'how many fewer'.
  9. Food wastage data can be shown using a bar graph, and we can calculate how many children could be fed from the wasted food.
  10. Always check the scale before answering any pictograph question — never assume one icon equals one item.
  11. In a bar graph, all bars must have the same width and be evenly spaced.
  12. True or false statements based on a picture require careful counting of every detail in the image.
  13. A table is a simple way to organize data in rows and columns before making a graph.
  14. Choosing a good scale (like 1 icon = 5 items) makes pictographs easier to draw and read.

MCQs — 10 Questions with Answers

Q1. In Joseph Uncle's toy shop, he used one picture to show 5 toys. If there are 3 pictures for toys, how many toys are there?

  • A. 8 toys
  • B. 15 toys ✓
  • C. 5 toys
  • D. 3 toys

Answer: B — With a scale of 1 picture = 5 toys, 3 pictures means 3 × 5 = 15 toys.

Q2. Deepti used one icon to show 3 two-wheelers. If she drew 4 icons for Monday, how many two-wheelers passed on Monday?

  • A. 7 two-wheelers
  • B. 12 two-wheelers ✓
  • C. 4 two-wheelers
  • D. 3 two-wheelers

Answer: B — With a scale of 1 icon = 3 two-wheelers, 4 icons means 4 × 3 = 12 two-wheelers.

Q3. What does a scale in a pictograph tell you?

  • A. The color of the pictures
  • B. How many items one picture represents ✓
  • C. The number of rows in the table
  • D. The date the data was collected

Answer: B — A scale shows what each icon or picture means, like 1 picture = 5 items.

Q4. In a bar graph showing daily routines, Raman's bar for sleeping reaches 8 hours and Sheela's reaches 6 hours. Who sleeps more?

  • A. Sheela sleeps more
  • B. Raman sleeps more ✓
  • C. Both sleep the same
  • D. Cannot tell from the graph

Answer: B — The height of the bar shows the number; Raman's bar is taller (8 > 6), so he sleeps more.

Q5. Which of the following is the main reason Joseph Uncle used a scale in his pictograph?

  • A. To make the shop look nice
  • B. To show large numbers using fewer pictures ✓
  • C. To confuse his customers
  • D. To change the color of icons

Answer: B — A scale reduces the number of pictures needed when showing large quantities like 100+ items.

Q6. In a pictograph, a half icon always represents ___.

  • A. Zero items
  • B. Exactly one item
  • C. Half of what one full icon represents ✓
  • D. The total number of items

Answer: C — A half icon shows half the scale value. If one full icon = 6 items, a half icon = 3 items.

Q7. In Sheela's bar graph of daily activities, the bar for 'studying' is shorter than the bar for 'sleeping.' What does this mean?

  • A. Studying is more important than sleeping
  • B. Sheela spends fewer hours studying than sleeping ✓
  • C. The graph is drawn incorrectly
  • D. Sheela does not like studying

Answer: B — In a bar graph, bar height directly shows the amount; shorter bar = smaller number of hours.

Q8. If food wastage data shows Sandwich wasted 8 kg and Idli-Sambar wasted 2 kg, which food was wasted the most?

  • A. Idli-Sambar
  • B. Sandwich ✓
  • C. Both equally
  • D. Cannot determine

Answer: B — Sandwich shows 8 kg > 2 kg of Idli-Sambar, so Sandwich had the most wastage.

Q9. Look at this pictograph scale: = 1 hour. If Raman's sleeping time shows 8 pictures, how many hours does he sleep?

  • A. 1 hour
  • B. 8 hours ✓
  • C. 16 hours
  • D. 4 hours

Answer: B — With scale 1 picture = 1 hour, 8 pictures means 8 × 1 = 8 hours of sleep.

Q10. What is the main difference between a pictograph and a bar graph?

  • A. Pictographs use colors; bar graphs use black and white
  • B. Pictographs use pictures/icons; bar graphs use vertical bars ✓
  • C. Pictographs are easier to draw than bar graphs
  • D. Bar graphs can only show numbers up to 10

Answer: B — The key difference is the visual representation: pictographs use icons while bar graphs use rectangular bars of different heights.

Flashcards

What is a pictograph?

A pictograph uses pictures or icons to show data in a way that is easy to understand and compare.

What does a scale mean in a pictograph?

A scale tells you what each icon represents, like one picture might mean 5 toys or 3 two-wheelers.

Why do we use a scale in pictographs?

A scale helps us show large numbers using fewer pictures, making the pictograph simple and clear.

What is a bar graph?

A bar graph uses vertical bars of different heights to show and compare amounts of different things.

How do you read a bar graph?

Look at the height of each bar and match it to the numbers on the vertical line to find the amount.

What is data?

Data is information we collect, count, or record, like how many children watch TV or how many toys are in a shop.

When should you use a pictograph instead of a bar graph?

Use a pictograph when you want a picture-based, fun way to show data; use a bar graph for more precise numbers.

What does a scale of 1 picture = 5 items mean?

Each picture or icon you draw stands for 5 real items, so 2 pictures mean 10 items.

How do you find the total using a pictograph with a scale?

Count the pictures for each item, multiply by the scale number, then add all the totals together.

What information do the axes of a bar graph show?

The horizontal axis shows the categories or names of items, and the vertical axis shows the numbers or amounts.

Important Board Questions

What is a scale in a pictograph? Give one example. [1 mark]

A scale shows what each picture represents. Example: 1 picture = 5 toys means one icon stands for 5 actual toys.

Joseph Uncle has 4 pictures of toys with a scale of 1 picture = 5 toys. How many toys does he have in total? [2 marks]

Multiply the number of pictures by the scale: 4 pictures × 5 toys per picture = total toys. Show your working.

Deepti recorded two-wheelers for three days using a pictograph with scale 1 icon = 3 two-wheelers. If Monday has 5 icons, Wednesday has 3 icons, and Friday has 6 icons, how many total two-wheelers did she record? Explain your steps. [3 marks]

For each day, multiply icons by 3. Then add all three totals together. Step 1: Find each day's count; Step 2: Add them all.

Raman and Sheela recorded their daily routines using a pictograph and a bar graph. Explain how they are different ways of showing the same information. Which method do you think is better for comparing sleeping hours and why? [5 marks]

Pictograph uses pictures with a scale; bar graph uses vertical bars with height showing numbers. For comparing exact hours, bar graphs show numbers more clearly because you read them directly from the vertical axis without multiplication.

True or False: If a pictograph uses a scale of 1 picture = 4 items, then 3 pictures represent 7 items. Explain your answer with correct working. [2 marks]

This is FALSE. Show that 3 × 4 = 12 items, not 7. Always multiply the number of pictures by the scale number.

Assertion-Reason Questions for Data Handling

Q1. Assertion (A):

A pictograph uses pictures or symbols to show data about things or events.

Reason (R):

Pictures are easier to understand than long lists of numbers.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains why pictographs use pictures — they are simpler and faster to understand at a glance than number lists.

Q2. Assertion (A):

When we use a scale like 1 icon = 5 items in a pictograph, we can show 25 items with 5 icons.

Reason (R):

A scale helps us record very large amounts of data using fewer icons.

Answer: B — Both A and R are true, but R is NOT the correct explanation of A — The assertion is true (25 ÷ 5 = 5 icons), but the reason does not explain this specific calculation. The reason explains the general purpose of using a scale, not why 25 items need 5 icons.

Q3. Assertion (A):

A bar graph shows data using rectangular bars of different heights or lengths.

Reason (R):

Bar graphs can only show information about animals and plants.

Answer: C — A is true but R is false — The assertion is true — bar graphs use bars to show quantities. However, the reason is false because bar graphs can show data about anything (time, food, toys, water, etc.), not just animals and plants.

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Case-Based Questions (CBQ) for Data Handling

Case Study:

Priya's family visited a fruit market. They bought 20 apples, 15 mangoes, and 10 bananas. Priya wanted to make a pictograph to show what they bought. She decided that 1 icon would represent 5 fruits. She drew the pictograph in her notebook showing the three types of fruits.

Q1. How many icons did Priya need to draw for apples if 1 icon = 5 fruits?

  • A. 3 icons
  • B. 4 icons ✓
  • C. 5 icons
  • D. 6 icons

Answer: B

Q2. How many icons did Priya need to draw for mangoes?

  • A. 2 icons
  • B. 3 icons ✓
  • C. 4 icons
  • D. 5 icons

Answer: B

Q3. How many total icons did Priya draw in her pictograph for all three fruits?

  • A. 6 icons
  • B. 7 icons
  • C. 8 icons
  • D. 9 icons ✓

Answer: D

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