Pictograph
Imagine a teacher asks everyone in the class about their favourite fruit. She gets answers like apple, banana, mango, and orange. Now she wants to show this information in a picture so that everyone can understand it quickly. She draws small pictures of fruits to show how many students chose each one. This is called a pictograph.
A pictograph (also called a picture graph) uses small pictures or symbols to represent data. Each picture stands for a certain number of items. It is one of the simplest ways to show information visually.
Pictographs make it easy to compare data at a glance. You can quickly see which group has the most or the least just by looking at the number of pictures.
What is Pictograph - Grade 6 Maths (Data Handling)?
Definition: A pictograph is a way of showing data using pictures or symbols, where each picture represents a fixed number of items.
Parts of a pictograph:
- Title — tells what the pictograph is about.
- Categories — the groups being compared (written on the left side or in rows).
- Pictures/Symbols — small images that represent the data.
- Key (Legend) — tells how many items each picture stands for. For example: 🍎 = 5 students.
Important:
- All pictures in a pictograph must be the same size.
- The key must always be given. Without the key, you cannot read the pictograph correctly.
- A half picture represents half the value of a full picture.
Pictograph Formula
Reading a pictograph:
Total value = Number of pictures × Value of each picture
Where:
- Number of pictures = count the symbols in that row.
- Value of each picture = the number given in the key.
Drawing a pictograph:
- Choose a symbol to represent the data.
- Decide the scale (key) — how many items each symbol stands for.
- Divide the data by the scale to find how many symbols to draw.
- Draw the symbols neatly in rows.
- Give a title and write the key.
Derivation and Proof
Example of reading a pictograph step by step:
A pictograph shows the number of books read by four students. The key says: 📖 = 4 books.
The data shows:
- Riya: 📖📖📖 (3 symbols)
- Aman: 📖📖📖📖📖 (5 symbols)
- Priya: 📖📖 (2 symbols)
- Karan: 📖📖📖📖 (4 symbols)
Reading the values:
- Riya: 3 × 4 = 12 books
- Aman: 5 × 4 = 20 books
- Priya: 2 × 4 = 8 books
- Karan: 4 × 4 = 16 books
Answering questions:
- Who read the most books? Aman (20 books — most symbols).
- Who read the least? Priya (8 books — fewest symbols).
- How many more books did Aman read than Priya? 20 − 8 = 12 books.
- Total books read by all = 12 + 20 + 8 + 16 = 56 books.
Types and Properties
Types of pictograph problems:
- Type 1: Reading a pictograph — Count the pictures, multiply by the key value, and answer questions.
- Type 2: Drawing a pictograph — Given raw data, choose a suitable key and draw the correct number of symbols.
- Type 3: Half symbols — When data does not divide evenly by the key, draw half a symbol. Example: If the key is 10 and the value is 25, draw 2 full symbols and one half symbol (2.5 symbols).
- Type 4: Choosing the right key — If numbers are large (like 100, 200, 300), choosing key = 50 or 100 makes the pictograph manageable.
- Type 5: Comparison questions — "How many more does A have than B?" or "Which category has the least?"
Solved Examples
Example 1: Example 1: Reading a Simple Pictograph
Problem: A pictograph shows toys sold by a shop. Key: ⭐ = 10 toys.
- Dolls: ⭐⭐⭐
- Cars: ⭐⭐⭐⭐⭐
- Balls: ⭐⭐
How many toys of each type were sold?
Solution:
- Dolls: 3 × 10 = 30 toys
- Cars: 5 × 10 = 50 toys
- Balls: 2 × 10 = 20 toys
Example 2: Example 2: Finding Total from a Pictograph
Problem: Using the pictograph from Example 1, find the total number of toys sold.
Solution:
- Total = 30 + 50 + 20
- Total = 100 toys
Example 3: Example 3: Comparing Categories
Problem: From Example 1, how many more cars were sold than balls?
Solution:
- Cars sold = 50
- Balls sold = 20
- Difference = 50 − 20 = 30 more cars
Example 4: Example 4: Using Half Symbols
Problem: A pictograph uses 🌟 = 10 students. A row shows 🌟🌟🌟 and half a 🌟. How many students does this represent?
Solution:
- 3 full symbols = 3 × 10 = 30
- Half symbol = 10 ÷ 2 = 5
- Total = 30 + 5 = 35 students
Example 5: Example 5: Drawing a Pictograph
Problem: The number of trees in four parks is: Park A = 20, Park B = 35, Park C = 15, Park D = 30. Draw a pictograph with key 🌳 = 5 trees.
Solution:
- Park A: 20 ÷ 5 = 4 symbols → 🌳🌳🌳🌳
- Park B: 35 ÷ 5 = 7 symbols → 🌳🌳🌳🌳🌳🌳🌳
- Park C: 15 ÷ 5 = 3 symbols → 🌳🌳🌳
- Park D: 30 ÷ 5 = 6 symbols → 🌳🌳🌳🌳🌳🌳
Write the title: "Number of Trees in Parks" and the key: 🌳 = 5 trees.
Example 6: Example 6: Choosing a Key
Problem: A school has 200 boys and 300 girls. Which key would be best: 1, 10, 50, or 100?
Solution:
- Key = 1: You would need 200 and 300 symbols. Too many!
- Key = 10: You would need 20 and 30 symbols. Still a lot.
- Key = 50: You would need 4 and 6 symbols. Good!
- Key = 100: You would need 2 and 3 symbols. Also good, but very few.
Answer: Key = 50 is the best choice (not too many, not too few symbols).
Example 7: Example 7: Finding the Value of One Symbol
Problem: A pictograph shows 6 symbols for Monday. The total for Monday is 30. What does each symbol represent?
Solution:
- 6 symbols = 30 items
- 1 symbol = 30 ÷ 6 = 5 items
Answer: Each symbol represents 5 items.
Example 8: Example 8: Finding How Many Symbols to Draw
Problem: In a pictograph, each symbol stands for 8 students. How many symbols will you draw for 56 students?
Solution:
- Number of symbols = 56 ÷ 8 = 7 symbols
Example 9: Example 9: Which Category Has the Most?
Problem: A pictograph shows: Red = 4 symbols, Blue = 7 symbols, Green = 3 symbols, Yellow = 5 symbols. Key: each symbol = 6 votes. Which colour is the most popular?
Solution:
- Red: 4 × 6 = 24 votes
- Blue: 7 × 6 = 42 votes
- Green: 3 × 6 = 18 votes
- Yellow: 5 × 6 = 30 votes
Answer: Blue is the most popular colour (42 votes).
Example 10: Example 10: Word Problem
Problem: A pictograph shows ice creams sold each day. Key: 🍦 = 20 ice creams. Monday has 3 symbols, Tuesday has 5 symbols, Wednesday has 4 symbols, Thursday has 2 symbols, Friday has 6 symbols. On which day were the most ice creams sold? Find the total for the week.
Solution:
- Monday: 3 × 20 = 60
- Tuesday: 5 × 20 = 100
- Wednesday: 4 × 20 = 80
- Thursday: 2 × 20 = 40
- Friday: 6 × 20 = 120
Most sold: Friday (120 ice creams).
Total: 60 + 100 + 80 + 40 + 120 = 400 ice creams.
Real-World Applications
Where are pictographs used?
- Newspapers and magazines — to show simple data like election results, sales figures, or survey results.
- Schools — to display attendance, favourite subjects, or sports day scores.
- Weather reports — small sun, cloud, or rain icons show the weather for each day.
- Shops and businesses — to show sales of different products in a visual way.
- Infographics — websites and social media use picture-based charts to make data interesting and easy to read.
- Government data — population, crop production, and other national data is sometimes shown using pictographs.
Key Points to Remember
- A pictograph uses pictures or symbols to represent data.
- Each picture stands for a fixed number of items (given in the key).
- To read a pictograph: count the pictures and multiply by the key value.
- A half picture means half the value of one full picture.
- Always include a title and a key when drawing a pictograph.
- All pictures should be the same size and neatly aligned.
- Choose a key that keeps the number of symbols manageable (not too many, not too few).
- Pictographs are best for simple data with few categories.
- For very large or detailed data, bar graphs are better than pictographs.
- Pictographs make it easy to compare data at a glance.
Practice Problems
- A pictograph shows the number of mangoes sold. Key: each symbol = 15 mangoes. Monday has 4 symbols and Tuesday has 6 symbols. How many mangoes were sold on each day?
- A pictograph uses a star symbol where each star = 12 students. How many symbols will you draw for 84 students?
- In a pictograph, 5 full symbols and one half symbol appear in a row. Each symbol = 20. What is the total?
- Choose a suitable key for this data: A = 100, B = 250, C = 150, D = 200.
- A pictograph shows favourite sports: Cricket = 8 symbols, Football = 5 symbols, Tennis = 3 symbols. Key = 10 students. Which sport is the least popular and how many students chose it?
- Draw a pictograph for: Apples = 40, Bananas = 25, Grapes = 15, Oranges = 30. Choose key = 5.
- Why must a pictograph always have a key?
- A pictograph has 3 symbols for Science and 7 symbols for Maths. If each symbol = 8 books, how many more Maths books are there than Science books?
Frequently Asked Questions
Q1. What is a pictograph?
A pictograph is a chart that uses small pictures or symbols to represent data. Each picture stands for a certain number of items. The number is shown in the key.
Q2. What is the key in a pictograph?
The key (also called legend) tells you how many items each picture represents. For example, if the key says each apple icon = 10, then 3 icons mean 30 apples.
Q3. What does a half symbol mean in a pictograph?
A half symbol means half the value of a full symbol. If each full symbol = 10, then a half symbol = 5.
Q4. How do you choose the right key?
Choose a key so that the number of symbols is manageable. If the data values are large (like 100, 200, 300), use a large key (like 50 or 100). If values are small (like 4, 8, 12), use a small key (like 2 or 4).
Q5. What is the difference between a pictograph and a bar graph?
A pictograph uses pictures to represent data. A bar graph uses rectangular bars. Bar graphs are more precise because you read the height of the bar on a scale. Pictographs are simpler but less precise.
Q6. Can a pictograph show fractions of items?
Yes, using half symbols. For example, if the key is 10 and the value is 15, draw 1 full symbol and 1 half symbol. Quarter symbols are rarely used because they are hard to draw clearly.
Q7. Why must all pictures be the same size?
If some pictures were bigger, you might think they represent more, which would be misleading. Same-sized pictures ensure fair comparison.
Q8. When should you use a pictograph instead of a table?
Use a pictograph when you want to make data easy to understand at a glance, especially for simple data with a few categories. Tables are better when you need exact numbers.
