Chapter 15 of Class 5 Maths, Data Through Pictures, covers data handling – collecting information, organising it using tally marks, and representing and interpreting it visually through pictographs and bar graphs.
Key Concepts
Collecting and Organising Data
Data is information collected about something, such as favourite fruits in a class or the number of vehicles passing by in an hour. Raw data is easier to understand once it is organised into a table or list.
Tally Marks
Tally marks are a quick way to count as data comes in – each item adds one vertical stroke, and every fifth stroke is drawn diagonally across the previous four to make groups of 5, which are then easy to count in fives.
Pictographs
A pictograph uses repeated pictures or symbols to represent data, where each picture stands for a fixed number of items (shown in a key, like “1 👍 = 5 students”). Counting the pictures for each category, using the key, gives the actual value.
Bar Graphs
A bar graph uses rectangular bars of different heights (or lengths) to represent data values, with a scale marked on one axis. Taller or longer bars represent bigger values, making comparisons between categories easy to see at a glance.
Reading and Interpreting Graphs
Reading a pictograph or bar graph means checking the key or scale first, then finding the value for each category, and using those values to answer questions like which category has the most, the least, or the total across all categories.
Choosing Between Pictograph and Bar Graph
A pictograph works well for smaller, whole-number-friendly data with a simple, visually engaging key, while a bar graph is more precise and flexible for a wider range of values, especially when exact and in-between values need to be shown clearly.
Worked Examples
Example 1: Reading a Pictograph
In a pictograph, each 🍒 symbol represents 4 apples sold. If the “Monday” row shows 3 symbols, how many apples were sold on Monday?
3 × 4 = 12 apples.
Example 2: Using Tally Marks
Convert the tally record |||| |||| || into a number.
Each group of 5 tally marks (shown as 4 strokes plus 1 diagonal) counts as 5: 5 + 5 + 2 = 12.
Example 3: Reading a Bar Graph
A bar graph shows favourite sports: Cricket bar reaches 25, Football bar reaches 18, Badminton bar reaches 12. Which sport is least popular, and what is the total of all three?
Badminton is least popular (12); total = 25 + 18 + 12 = 55 students.
Quick Recap
- Tally marks group counts in fives, making them quick to record and to add up.
- A pictograph uses repeated symbols, each worth a fixed number shown in a key.
- A bar graph uses bars of different heights/lengths against a marked scale to show and compare values.
- Always check the key (pictograph) or scale (bar graph) before reading any values from a graph.
- Bar graphs are generally more precise for a wide range of values than pictographs.
Common Mistakes to Avoid
- Forgetting to multiply by the key value when reading a pictograph (counting the number of symbols as the final answer instead of the value they represent).
- Miscounting tally groups, especially forgetting that the fifth mark is drawn diagonally across the first four.
- Misreading the scale on a bar graph, especially when each gridline does not represent exactly 1 unit.
- Comparing bars without checking they are drawn against the same, single scale.
- Leaving out a partial symbol in a pictograph, which usually represents a value smaller than the full key amount (e.g. half a symbol = half the key value).
Home Practice Tips
- Survey family members’ favourite fruit, colour, or season, record the results using tally marks, and total them.
- Turn a simple survey into a pictograph using a fixed symbol and key, then into a bar graph, and compare how each looks.
- Read a bar graph or pictograph from a newspaper, textbook, or website together, and practise answering “most,” “least,” and “total” questions about it.
- Count and tally everyday objects at home (types of fruit in a basket, books on a shelf by subject) as a quick data-collection exercise.
- Practise drawing bars to scale on graph paper for a small set of numbers, like weekly pocket money or hours spent on different activities.
Frequently Asked Questions
Q1. Why do we group tally marks in fives?
Grouping in fives makes large collections of tally marks much easier and faster to count at a glance, since groups of five can simply be added in multiples of five instead of counting each individual mark.
Q2. Why does a pictograph need a key?
Because each picture symbol represents more than one item in many cases, and without the key stating exactly how many, the pictograph’s symbols would be impossible to interpret accurately.
Q3. When is a bar graph better than a pictograph?
When data involves a wide range of values or values that don’t divide evenly by a simple key number, a bar graph (with a numbered scale) gives a more precise and flexible way to represent and compare the data.
Q4. How do I find the total from a bar graph?
Read the value each bar represents using the scale, then add all those values together.
Q5. What’s the difference between collecting data and representing data?
Collecting data means gathering the raw information (like counting responses in a survey), while representing data means organising and displaying that information visually, such as in a tally chart, pictograph, or bar graph, to make it easier to understand and compare.
Full walkthrough: Chapter 15 Solutions · Extra Questions.
Recommended: Buy the Printed NCERT Class 5 Maths Book
Contains Amazon affiliate links.
If you’d like a printed copy alongside the PDF, here’s a verified option:
Check the latest price on Amazon
Price and availability may change on Amazon. As an Amazon Associate, ncertbooks.org earns from qualifying purchases.
