Notes For All Chapters – Maths Class 6 Ganita Prakash
📊 Ganita Prakash • Grade 6
📊 Chapter 4: Data Handling and Presentation
Learn to collect, organise, and display data using tally marks, pictographs, and bar graphs!
Data Collection
Tally Marks
Frequency Tables
Pictographs
Bar Graphs
Scale & Key
Infographics
Tally Marks
Frequency Tables
Pictographs
Bar Graphs
Scale & Key
Infographics
📋 Contents
- Introduction — What is Data?
- 4.1 Collecting and Organising Data
- Tally Marks & Frequency
- 4.2 Pictographs
- Drawing a Pictograph
- 4.3 Bar Graphs
- 4.4 Drawing a Bar Graph
- Choosing the Right Scale
- 4.5 Artistic & Aesthetic Considerations
- Infographics
- Pictograph vs Bar Graph
- Chapter Summary
- Exam Practice Questions
Introduction — What is Data?
We live in an age of information! Every day we see numbers and facts around us — weather reports, cricket scores, population figures. All of this is data.
📊 DATA = Any collection of facts, numbers, measures, observations, or descriptions that convey information about things.
🌟 Examples of Data
- A list of favourite colours of your classmates
- The weights of all students in your class
- The number of goals scored in each football match
- Daily temperatures for a week
- Number of books read by each student in a month
Why do we study data handling?
Raw data (a big list of numbers) is hard to understand at a glance. By organising and presenting it in smart ways — tables, graphs, pictographs — we can quickly find patterns, make comparisons, and draw conclusions!
Raw data (a big list of numbers) is hard to understand at a glance. By organising and presenting it in smart ways — tables, graphs, pictographs — we can quickly find patterns, make comparisons, and draw conclusions!
📋 When do we need to collect data?
✅ Data collection needed:
“What is the most popular TV show in our class?” — We must ask everyone to find out.
“What is the most popular TV show in our class?” — We must ask everyone to find out.
❌ No data collection needed:
“What is the capital of India?” — This is already known. No collection required!
“What is the capital of India?” — This is already known. No collection required!
✅ Data collection needed:
“How much water is wasted in our locality?” — We must measure or survey to find out.
“How much water is wasted in our locality?” — We must measure or survey to find out.
❌ No data collection needed:
“When did India get independence?” — This is a historical fact. Already known!
“When did India get independence?” — This is a historical fact. Already known!
4.1 Collecting and Organising Data
Navya and Naresh wanted to know which game was most popular in their class. They asked every student and made a list. But a long list is hard to read! We need to organise data to understand it easily.
How to find the most popular item from a list?
Count how many times each item appears. The one with the highest count is the most popular. This count is called the frequency.
Count how many times each item appears. The one with the highest count is the most popular. This count is called the frequency.
📊 Navya’s Class — Favourite Games
| Game | Number of Students (Frequency) |
|---|---|
| Cricket | 6 |
| Hockey | 8 ← Most Popular! 🏆 |
| Kabaddi | 6 |
| Satoliya (Pittu) | 6 |
| Football | 4 |
| Badminton | 2 |
Key Term — FREQUENCY:
The frequency of a value is the number of times it appears in the data. Example: Hockey appears 8 times → Frequency of Hockey = 8.
The frequency of a value is the number of times it appears in the data. Example: Hockey appears 8 times → Frequency of Hockey = 8.
📐 Arranging Data in Ascending Order
Sushri Sandhya collected shoe sizes: 4, 5, 3, 4, 3, 4, 5, 5, 4, 5, 5, 4, 5, 6, 4, 3, 5, 6, 4, 6, 4, 5, 7, 5, 6, 4, 5
After arranging in ascending order: 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7
Largest shoe size: 7 (last in the arranged list)
Smallest shoe size: 3 (first in the arranged list)
Students with size 5: Count the 5s → 10 students
Sizes larger than 4: Count 5s, 6s, 7s → 10+4+1 = 15 students
Why arrange data in ascending order?
It makes it very easy to find the minimum, maximum, range, and count specific values. Sorted data is organised data!
It makes it very easy to find the minimum, maximum, range, and count specific values. Sorted data is organised data!
Tally Marks and Frequency Tables
Tally marks are a quick way to count data as it is being collected. Instead of writing numbers, we draw vertical lines and cross every 5th one.
📝 Tally Mark System:
| = 1 || = 2 ||| = 3 |||| = 4 |||| = 5 (four lines with one crossing through)
| = 1 || = 2 ||| = 3 |||| = 4 |||| = 5 (four lines with one crossing through)
Each bundle of 5 is written as ╫ (4 lines + 1 diagonal cross)
🍬 Shri Nilesh’s Sweet Preference Table
| Sweet | Tally Marks | Frequency (No. of Students) |
|---|---|---|
| 🟡 Jalebi | ╫ | | 6 |
| 🟤 Gulab Jamun | ╫ |||| | 9 |
| 🟠 Gujiya | ╫ ╫ ||| | 13 ← Most Popular! |
| 🩷 Barfi | ||| | 3 |
| ⚪ Rasgulla | ╫ || | 7 |
Why use tally marks?
Tally marks are faster to draw than writing numbers, and grouping by 5 makes it easy to count totals quickly. They help avoid miscounting in long lists.
Tally marks are faster to draw than writing numbers, and grouping by 5 makes it easy to count totals quickly. They help avoid miscounting in long lists.
Important Limitation of Frequency Tables:
A frequency table tells you HOW MANY people chose each item, but NOT which specific person chose what. For example, we know 6 students chose Jalebi, but not their names. If we need to give each person their correct sweet, we need the original name-wise list!
A frequency table tells you HOW MANY people chose each item, but NOT which specific person chose what. For example, we know 6 students chose Jalebi, but not their names. If we need to give each person their correct sweet, we need the original name-wise list!
📊 How to Make a Frequency Table
- List all the categories/values in the first column
- Go through the raw data one item at a time
- For each item, put a tally mark (|) next to the correct category
- After every 4 tally marks, the 5th one crosses them (╫)
- Count the tally marks for each category and write the frequency
4.2 Pictographs
🖼️ A PICTOGRAPH represents data using pictures or symbols, where each picture stands for a certain number of items. It helps you understand data at a quick glance!
🚌 Example — Modes of Travel (1 symbol = 1 student)
| Mode of Travel | Number of Students (😊 = 1 student) | Count |
|---|---|---|
| 🚗 Private Car | 😊😊😊😊 | 4 |
| 🚌 Public Bus | 😊😊😊😊😊 | 5 |
| 🏫 School Bus | 😊😊😊😊😊😊😊😊😊😊😊 | 11 ← Most! |
| 🚲 Cycle | 😊😊😊 | 3 |
| 🚶 Walking | 😊😊😊😊😊😊😊 | 7 |
🔑 The Scale / Key in Pictographs
When data numbers are large, one symbol can represent multiple items. This is called the scale or key.
Small scale (1 symbol = 1 item)
Good for small datasets. Easy and accurate. Too many symbols for large data.
Good for small datasets. Easy and accurate. Too many symbols for large data.
Medium scale (1 symbol = 5 items)
Good for medium datasets. Fewer symbols needed. Half symbol = 2.5 items.
Good for medium datasets. Fewer symbols needed. Half symbol = 2.5 items.
Large scale (1 symbol = 10 items)
Good for large datasets. Very compact. Half symbol = 5 items.
Good for large datasets. Very compact. Half symbol = 5 items.
Half symbol trick 🌗
When a value isn’t an exact multiple of the scale, use half a symbol. e.g., if scale = 10 and value = 25, draw 2 full + 1 half symbol.
When a value isn’t an exact multiple of the scale, use half a symbol. e.g., if scale = 10 and value = 25, draw 2 full + 1 half symbol.
Reading Pictographs — Nand Kishor’s Sleep Survey (Scale = 10 children per symbol):
Always → 5 symbols → 5 × 10 = 50 children
Sometimes → 2 full + half → (2 × 10) + 5 = 25 children
Never → 4 symbols → 4 × 10 = 40 children
Formula to read a pictograph:
Actual value = (Number of complete symbols × scale) + (Number of half symbols × scale ÷ 2)
✅ Properties of a Good Pictograph
- Has a clear title at the top
- Has a key/scale showing what each symbol represents
- Uses the same symbol throughout
- Categories are equally spaced (horizontal or vertical arrangement)
- Symbols are neatly drawn in rows/columns
Challenge with pictographs:
When values are NOT exact multiples of the scale, it’s hard to draw exact fractions of symbols. For example, if scale = 10 and value = 33, how do you draw 3.3 symbols? This is a limitation of pictographs!
When values are NOT exact multiples of the scale, it’s hard to draw exact fractions of symbols. For example, if scale = 10 and value = 33, how do you draw 3.3 symbols? This is a limitation of pictographs!
Drawing a Pictograph — Step by Step
📝 Steps to Draw a Pictograph
- Collect and organise data into a frequency table first
- Choose a suitable symbol that relates to the data (e.g., 🪁 for kites)
- Decide the scale/key — how many items each symbol represents. Choose a scale that avoids too many fractions. Rule: Scale = a factor of the largest value
- Draw the table with categories in rows/columns
- Draw the symbols for each category based on the scale
- Add the key/legend clearly (e.g., 🪁 = 100 kites)
- Add a title to the pictograph
🪁 Example — Magan Bhai’s Kite Sales (Scale: 1 symbol = 100 kites)
| Shopkeeper | Kites Sold | Symbols (🪁 = 100 kites) |
|---|---|---|
| Chaman | 250 | 🪁🪁🌗 |
| Rani | 300 | 🪁🪁🪁 |
| Rukhsana | 100 | 🪁 |
| Jasmeet | 450 | 🪁🪁🪁🪁🌗 |
| Jetha Lal | 250 | 🪁🪁🌗 |
| Poonam Ben | 700 | 🪁🪁🪁🪁🪁🪁🪁 |
Quick answers from this pictograph:
Rani: 300 ÷ 100 = 3 symbols. Maximum buyer: Poonam Ben (700 kites). Jasmeet (450) > Chaman (250). Poonam Ben (700) = more than double Rani (300) ✓ (700 > 2×300=600).
Rani: 300 ÷ 100 = 3 symbols. Maximum buyer: Poonam Ben (700 kites). Jasmeet (450) > Chaman (250). Poonam Ben (700) = more than double Rani (300) ✓ (700 > 2×300=600).
4.3 Bar Graphs
📊 A BAR GRAPH represents data using rectangular bars of equal width. The height (or length) of each bar shows the frequency or value for that category. A scale is used to read the exact values.
Bar graphs are better than pictographs when dealing with large numbers or when values are not nice multiples of a symbol value. They give a more precise visual comparison.
📊 Example — Students Absent per Class (Bar Graph)
Reading this bar graph:
Class 5 had zero absences (full attendance). Class 8 had the most absences (7 students). Classes 2 and 7 both had 5 absences each.
Class 5 had zero absences (full attendance). Class 8 had the most absences (7 students). Classes 2 and 7 both had 5 absences each.
🚗 Delhi Traffic — Horizontal Bar Graph (Scale: 1 unit = 100 vehicles)
Why is traffic heaviest at 7–8 AM?
This is when people travel to offices, schools, and markets. After 8 AM, traffic decreases as people have already reached their destinations. Before 7 AM, most people are still asleep!
This is when people travel to offices, schools, and markets. After 8 AM, traffic decreases as people have already reached their destinations. Before 7 AM, most people are still asleep!
4.4 Drawing a Bar Graph — Step by Step
- Draw two perpendicular lines — one horizontal (X-axis) and one vertical (Y-axis)
- Write the categories along the X-axis with equal spacing
- Choose a scale for the Y-axis (e.g., 1 unit = 1 student or 1 unit = ₹200)
- Mark the values on Y-axis starting from 0
- Draw bars of equal width with equal gaps between them
- The height of each bar = frequency ÷ scale value
- Add a title and axis labels
🍬 Sweet Preferences Bar Graph — Height Calculation
| Sweet | Frequency | Scale: 1 unit = 1 student | Bar Height |
|---|---|---|---|
| Jalebi | 6 | 6 ÷ 1 | 6 units |
| Gulab Jamun | 9 | 9 ÷ 1 | 9 units |
| Gujiya | 13 | 13 ÷ 1 | 13 units ← Tallest! |
| Barfi | 3 | 3 ÷ 1 | 3 units ← Shortest |
| Rasgulla | 7 | 7 ÷ 1 | 7 units |
🏏 Smriti’s Runs — Larger Scale Needed
When frequencies are large, using scale 1:1 would make the bar too long. We need a bigger scale.
| Match | Runs Scored | Scale: 1 unit = 10 runs | Bar Height |
|---|---|---|---|
| Match 1 | 80 | 80 ÷ 10 | 8 units |
| Match 2 | 50 | 50 ÷ 10 | 5 units |
| Match 3 | 10 | 10 ÷ 10 | 1 unit |
| Match 4 | 100 | 100 ÷ 10 | 10 units ← Highest |
| Match 5 | 90 | 90 ÷ 10 | 9 units |
| Match 6 | 0 | 0 ÷ 10 | 0 units (no bar) |
| Match 7 | 90 | 90 ÷ 10 | 9 units |
| Match 8 | 50 | 50 ÷ 10 | 5 units |
🏠 Imran’s Family Budget — Choosing Scale = ₹200
| Item | Expenditure (₹) | Calculation | Bar Height (units) |
|---|---|---|---|
| House Rent | ₹3000 | 3000 ÷ 200 | 15 units |
| Food | ₹3400 | 3400 ÷ 200 | 17 units ← Highest! |
| Education | ₹800 | 800 ÷ 200 | 4 units |
| Electricity | ₹400 | 400 ÷ 200 | 2 units ← Lowest! |
| Transport | ₹600 | 600 ÷ 200 | 3 units |
| Miscellaneous | ₹1200 | 1200 ÷ 200 | 6 units |
From Imran’s bar graph:
Most spent: Food (₹3400). Second most: House Rent (₹3000). Electricity (₹400) = half of Education (₹800)? 400 = 800÷2 ✓ Yes! Education (₹800) vs Food (₹3400): 800 < 3400÷4 = 850 ✓ Yes, education costs less than one-fourth of food!
Most spent: Food (₹3400). Second most: House Rent (₹3000). Electricity (₹400) = half of Education (₹800)? 400 = 800÷2 ✓ Yes! Education (₹800) vs Food (₹3400): 800 < 3400÷4 = 850 ✓ Yes, education costs less than one-fourth of food!
Choosing the Right Scale
Choosing the right scale is crucial — too small and the graph is enormous, too large and details are lost.
🔑 Scale Rule: Choose a scale so that the largest bar fits nicely on your paper AND the scale value divides most data values evenly (few fractions).
🔢 How to Choose Scale
- Find the maximum value in the data
- Decide how tall/long you want the longest bar to be (e.g., 10–15 cm on paper)
- Divide: Scale = maximum value ÷ desired bar length
- Round the scale to a “nice” number (5, 10, 20, 50, 100, 200, 500…)
- Check that other values also come out as whole numbers or simple fractions
📊 Scale Examples
Data: max = 13 students
Scale = 1 unit = 1 student
Bar height = 13 units ✓ Easy!
Scale = 1 unit = 1 student
Bar height = 13 units ✓ Easy!
Data: max = 100 runs
Scale = 1 unit = 10 runs
Bar height = 10 units ✓ Manageable!
Scale = 1 unit = 10 runs
Bar height = 10 units ✓ Manageable!
Data: max = 3400 rupees
Scale = 1 unit = 200 rupees
Bar height = 17 units ✓ Fits on paper!
Scale = 1 unit = 200 rupees
Bar height = 17 units ✓ Fits on paper!
Data: max = 102 crore people
Scale = 1 unit = 10 crore
Bar height = ~10 units ✓ Perfect!
Scale = 1 unit = 10 crore
Bar height = ~10 units ✓ Perfect!
Scale must ALWAYS start from ZERO!
The Y-axis markings must start from 0. If you start from a different number, the graph becomes misleading — bars will look bigger or smaller than they really are!
The Y-axis markings must start from 0. If you start from a different number, the graph becomes misleading — bars will look bigger or smaller than they really are!
4.5 Artistic and Aesthetic Considerations
Beyond accuracy, a good data presentation should also be visually appealing and easy to understand for its audience.
🎨 A good graph should be: Accurate + Clear + Visually appealing + Appropriately sized
🏔️ Vertical vs Horizontal Bars — When to Use Which?
📊 Horizontal Bars
- Use for data that extends sideways (distances, lengths)
- More intuitive for things measured along the ground
- Example: Lengths of rivers — bars extend horizontally like rivers!
- Also better when category labels are long
Tallest Mountains on Each Continent:
Asia: Everest (8848m) > S.America: Aconcagua (6962m) > N.America: Denali (6194m) > Africa: Kilimanjaro (5895m) > Europe: Elbrus (5642m) > Antarctica: Vinson Massif (4892m) > Australia: Koscuiszko (2228m)
Everest is 8848 − 2228 = 6620m taller than Koscuiszko!
🎨 Making Graphs Visually Appealing
- Use colours to distinguish different bars
- Add a clear, descriptive title
- Label both axes clearly with units
- Choose an appropriate scale so the graph fits well on the page
- Keep bars of equal width and equal spacing
- Ensure bars start from zero on the axis
Infographics — When Art Meets Data
🌟 INFOGRAPHIC = Information + Graphic. When bar graphs and data visualisations are further beautified with artistic imagery, colours, and creative shapes, they become infographics.
The goal of infographics is to make data even more engaging and instantly understandable — like using triangle shapes for mountain heights or wave shapes for river lengths.
The Danger of “Fancy” Infographics!
Pretty can be misleading! When triangles are used to show mountain heights, taller triangles are also WIDER. This implies taller mountains are wider too — which may not be true! The extra width gives a false visual impression that the difference is bigger than it really is.
Pretty can be misleading! When triangles are used to show mountain heights, taller triangles are also WIDER. This implies taller mountains are wider too — which may not be true! The extra width gives a false visual impression that the difference is bigger than it really is.
Critical Thinking about Infographics:
Always ask: “Does the visual accurately represent ONLY the data dimension being compared?”
In a bar graph, we compare ONE dimension (height = frequency). But if the visual shows mountains of varying width AND height, it’s comparing TWO dimensions — misleading!
Always ask: “Does the visual accurately represent ONLY the data dimension being compared?”
In a bar graph, we compare ONE dimension (height = frequency). But if the visual shows mountains of varying width AND height, it’s comparing TWO dimensions — misleading!
What is 5642 × 2 = 11,284? Everest (8848m) is NOT twice as tall as Elbrus (5642m)!
📋 Rules for Good Infographics
- Accuracy first — beauty second
- Only one visual dimension should change to show quantity (usually length/height)
- Width, area, or volume should NOT change unless they represent additional data
- Always include a scale/key so viewers can verify the numbers
- Be especially careful with 3D effects — they distort perceived sizes!
Pictograph vs Bar Graph — Quick Comparison
| Feature | Pictograph | Bar Graph |
|---|---|---|
| Representation | Pictures/symbols | Rectangular bars |
| Visual appeal | More colourful/fun | Clean and precise |
| Scale | 1 symbol = N items | 1 unit length = N items |
| Best for | Small, round numbers | Any numbers, large datasets |
| Limitation | Fractions of symbols are hard to draw | Less visually engaging |
| Precision | Less precise | More precise |
| Easy to draw? | Takes more time (drawing symbols) | Faster to draw |
| Both must have | Title + Key/Scale | Title + Scale + Axis Labels |
🐯
India’s Tiger Population — Real Data!
Project Tiger launched in 1973 to protect India’s tigers. In 2006: ~1400 tigers. 2010: ~1700. 2014: ~2200. 2018: ~3000. 2022: ~3700! The population has more than doubled in 16 years — a great conservation success story! A bar graph clearly shows this upward trend.
Project Tiger launched in 1973 to protect India’s tigers. In 2006: ~1400 tigers. 2010: ~1700. 2014: ~2200. 2018: ~3000. 2022: ~3700! The population has more than doubled in 16 years — a great conservation success story! A bar graph clearly shows this upward trend.
Chapter Summary
📊 Data
Any collection of facts, numbers, measures or observations that conveys information. We collect data to answer specific questions.
Any collection of facts, numbers, measures or observations that conveys information. We collect data to answer specific questions.
✏️ Tally Marks
A fast way to count. Groups of 5 (╫) make counting easy. The total counts are called frequencies.
A fast way to count. Groups of 5 (╫) make counting easy. The total counts are called frequencies.
📋 Frequency Table
Organises raw data into categories with their frequencies. Shows which category appears most/least.
Organises raw data into categories with their frequencies. Shows which category appears most/least.
🖼️ Pictograph
Uses pictures/symbols to show data. Each symbol = scale value. Half symbol = half the scale value. Best for small, round numbers.
Uses pictures/symbols to show data. Each symbol = scale value. Half symbol = half the scale value. Best for small, round numbers.
📊 Bar Graph
Uses rectangular bars of equal width. Bar height = frequency. Must start from zero. More precise than pictographs.
Uses rectangular bars of equal width. Bar height = frequency. Must start from zero. More precise than pictographs.
🔑 Scale
Both pictographs and bar graphs need a scale/key. Choose a scale that fits the data neatly and doesn’t cause too many fractions.
Both pictographs and bar graphs need a scale/key. Choose a scale that fits the data neatly and doesn’t cause too many fractions.
📊 Vertical vs Horizontal
Vertical bars (column graphs) for heights/quantities. Horizontal bars for lengths/distances. Match the bar direction to the data type!
Vertical bars (column graphs) for heights/quantities. Horizontal bars for lengths/distances. Match the bar direction to the data type!
🌟 Infographics
Visually beautified data representations. More engaging but can be misleading if not done carefully. Accuracy must always come first!
Visually beautified data representations. More engaging but can be misleading if not done carefully. Accuracy must always come first!
⬆️ Ascending Order
Arranging data from smallest to largest helps quickly identify minimum, maximum, and count specific values.
Arranging data from smallest to largest helps quickly identify minimum, maximum, and count specific values.
📏 Reading Graphs
Find max (tallest bar), min (shortest bar), compare categories, and calculate totals by adding bar values.
Find max (tallest bar), min (shortest bar), compare categories, and calculate totals by adding bar values.
🎨 Good Presentation
A good graph is: accurate, clearly titled, has labelled axes, appropriate scale starting from 0, and is visually appealing.
A good graph is: accurate, clearly titled, has labelled axes, appropriate scale starting from 0, and is visually appealing.
⚠️ Misleading Graphs
Too much artistic decoration can mislead viewers. Always check if the visual change (size, area) correctly represents ONLY the data being shown.
Too much artistic decoration can mislead viewers. Always check if the visual change (size, area) correctly represents ONLY the data being shown.
Exam Practice Questions
Q1. What is data? Give two examples of data you might collect in your school.
Ans: Data is any collection of facts, numbers, or observations that gives us information. Examples: (1) Favourite sports of all students in the school. (2) The number of books each student reads per month. ✓
Q2. In a survey, 30 students were asked their favourite subject. The results (tally): Maths ╫╫╫, Science ╫╫||, English ╫|||||, Hindi ╫||. Complete the frequency table and find the most and least popular subjects.
Ans: Maths = 15, Science = 12, English = 10, Hindi = 7. Most popular: Maths (15 students). Least popular: Hindi (7 students). ✓
Q3. In a pictograph, 1 symbol 🌸 = 5 flowers. A garden has: Row A = 🌸🌸🌸🌸, Row B = 🌸🌸🌸🌸🌸🌗, Row C = 🌸🌸. How many flowers are in each row? Which row has the most?
Ans: Row A = 4 × 5 = 20 flowers. Row B = (5 × 5) + (½ × 5) = 25 + 2.5 = 27.5 ≈ 27 or 25+2 = 27 flowers (half symbol = 2-3 flowers if scale=5). Row C = 2 × 5 = 10 flowers. Row B has the most flowers. ✓
Q4. The following data shows runs scored by a team in 5 matches: 40, 80, 60, 100, 20. If scale = 1 unit = 20 runs, calculate the bar heights for each match.
Ans: Match 1: 40÷20 = 2 units. Match 2: 80÷20 = 4 units. Match 3: 60÷20 = 3 units. Match 4: 100÷20 = 5 units (tallest). Match 5: 20÷20 = 1 unit (shortest). ✓
Q5. Why should the scale on a bar graph always start from zero?
Ans: If the scale doesn’t start from zero, bars will appear larger or smaller than their actual difference. For example, if Y-axis starts at 50, a bar at 60 appears much taller than one at 55, when the actual difference is only 5. Starting from zero ensures bars accurately represent the real proportional differences in the data. ✓
Q6. Shoe sizes of 10 students: 5, 4, 6, 5, 4, 5, 6, 4, 5, 4. Arrange in ascending order and prepare a frequency table. What is the most common shoe size?
Ans: Ascending order: 4, 4, 4, 4, 5, 5, 5, 5, 6, 6. Frequency table: Size 4 → 4 students, Size 5 → 4 students, Size 6 → 2 students. Most common: Size 4 and Size 5 (both appear 4 times — tied!). ✓
Q7. For a pictograph of kite sales with values 250, 300, 100, 450, 700: What is the best scale to use? Why not use scale = 1 symbol = 1 kite?
Ans: Best scale = 1 symbol = 50 kites (all values are multiples of 50). Scale 1:1 is impractical because the largest value (700) would need 700 symbols — too many to draw! A scale of 50 or 100 reduces symbols to 7–14, which is manageable. ✓
Q8. When would you prefer a bar graph over a pictograph? Give two reasons.
Ans: (1) When data values are large and not exact multiples of a nice scale — drawing fractions of symbols in a pictograph is difficult, but partial bars are easy to estimate. (2) When you need to read precise values — bar heights can be read accurately from the scale, while symbol fractions are approximate. ✓
Q9. What is an infographic? Give one advantage and one disadvantage compared to a plain bar graph.
Ans: An infographic is a visually enriched data representation that uses artistic imagery, colours, and creative shapes to make data more engaging. Advantage: More visually appealing and attention-grabbing; communicates information more memorably. Disadvantage: Can be misleading — e.g., using triangles for mountains makes taller bars also wider, implying extra information that may be inaccurate. ✓
Q10. A bar graph of monthly rainfall shows: Jan=20mm, Feb=15mm, Mar=30mm, Apr=5mm. Total? Which month had the most rain? Which had the least?
Ans: Total = 20 + 15 + 30 + 5 = 70 mm. Most rain: March (30mm — tallest bar). Least rain: April (5mm — shortest bar). ✓
Please give full and detailed notes on chapter
One of the best for any one as it is full of cheering
infographic definition