Class 6 Maths · Original EZT practice
Data Handling and Presentation (Class 6 Chapter 4): summary and practice
Ask a class for favourite colours and you get a list - that list is data. Chapter 4 shows how to organise data with tally marks, show it as pictographs and bar graphs, and read it back. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 6). Older Class 6 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Collecting and organising data
Data is a collection of facts such as counts or names. A tally mark records each item, bundled in fives (four lines and a fifth across). The number of times an item occurs is its frequency; a frequency table lists items with their counts.
2. Pictographs
A pictograph uses a picture or symbol to stand for a number of items. Always read the key first: if one symbol stands for five books, three symbols mean fifteen.
3. Bar graphs
A bar graph uses bars of equal width, with heights showing the counts. The scale on the vertical axis decides how tall each bar looks; choose a scale that fits the largest value.
4. Drawing a bar graph and presenting it well
Steps: pick a scale (say one square stands for two units), draw and label both axes, draw bars of equal width with equal gaps, and give the graph a title. Neat labels and a clear title make a graph easy to read.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Make a frequency table from raw votes
Choose the method: Count each item one by one, then list items with their counts.
EZT practice question
Votes for a class snack: samosa, fruit, samosa, sandwich, samosa, fruit, sandwich, samosa. Make the frequency table.
Show the worked solution
- Count samosas: four votes.
- Count fruit: two votes.
- Count sandwiches: two votes.
- Total: eight votes, matching the list.
Answer: Samosa four, fruit two, sandwich two - eight votes in all.
Check: The counts add up to the number of votes in the raw list.
Watch for this: Do not stop counting halfway; tally every entry once and only once.
Now try it yourself
What is frequency?
Check your answer
The number of times an item occurs in the data.
That is the chapter's definition of frequency.
Write numbers in tally marks
Choose the method: Bundle in fives: four lines, then the fifth across.
EZT practice question
How do you write seven in tally marks?
Show the worked solution
- Make one full bundle of five.
- Add two single lines after it.
Answer: One bundle of five and two single lines.
Check: Five plus two gives seven.
Watch for this: Do not draw seven separate lines; bundles of five are what make tallies quick to read.
Now try it yourself
Tabulate these votes: red, blue, red, red, green, blue.
Check your answer
Red three, blue two, green one.
Counting each colour once gives its frequency.
Read a pictograph using its key
Choose the method: Multiply the number of symbols by the value in the key.
EZT practice question
In a pictograph, one star stands for ten students. A class has four stars. How many students?
Show the worked solution
- The key says one star means ten students.
- Four stars mean four times ten.
Answer: Forty students - four times ten.
Check: Symbol count times the key value gives the total.
Watch for this: Do not count the stars themselves as students; read the key first.
Now try it yourself
One flag stands for six pencils. How many pencils do five flags show?
Check your answer
Thirty pencils.
Five times six is thirty.
Handle half symbols in a pictograph
Choose the method: A half symbol stands for half the key value.
EZT practice question
If one symbol stands for four items and a row shows two and a half symbols, how many items?
Show the worked solution
- Two full symbols mean two times four, that is eight.
- Half a symbol means half of four, that is two.
- Eight plus two is ten.
Answer: Ten items - two and a half times four.
Check: The half symbol contributes exactly half the key value.
Watch for this: Do not ignore the half symbol or count it as a whole one.
Now try it yourself
Why must the key be given with a pictograph?
Check your answer
It tells what one symbol stands for.
Without the key, the symbols cannot be converted into counts.
Compare values on a bar graph
Choose the method: Compare bar heights; subtract for differences.
EZT practice question
Bars for books read: Anu twelve, Ravi eight, Sia fifteen. Who read the most and by how many more than Ravi?
Show the worked solution
- The tallest bar is Sia's at fifteen.
- Fifteen minus eight is seven.
Answer: Sia read the most - seven more than Ravi.
Check: The tallest bar gives the most; the difference comes from subtraction.
Watch for this: Do not compare with Anu when the question asks about Ravi.
Now try it yourself
What does the height of a bar show?
Check your answer
The count or value for that item.
In a bar graph the height carries the number.
Find a total from bar heights
Choose the method: Add the values the bars show.
EZT practice question
Find the total books read by Anu, Ravi and Sia from the same bars.
Show the worked solution
- Anu read twelve, Ravi eight, Sia fifteen.
- Twelve plus eight plus fifteen is thirty-five.
Answer: Thirty-five books in total.
Check: Adding the three bar values gives the combined total.
Watch for this: Do not average the bars when a total is asked; add them.
Now try it yourself
Scores twenty, thirty-five, twenty-five - which bar is tallest and what is the difference between tallest and shortest?
Check your answer
The thirty-five bar is tallest; the difference is fifteen.
Thirty-five minus twenty is fifteen.
Choose a scale that fits the largest value
Choose the method: Divide the largest value by the available squares to get units per square.
EZT practice question
Choose a scale for values four, ten, sixteen, twenty on a graph with ten squares of height.
Show the worked solution
- The largest value is twenty.
- Twenty divided by ten squares gives two units per square.
- So one square stands for two units: bars are two, five, eight and ten squares tall.
Answer: One square stands for two units - the bars are two, five, eight and ten squares tall.
Check: The largest bar exactly fills the ten squares, so the scale fits.
Watch for this: Do not pick one square per unit; twenty units would need twenty squares and overflow.
Now try it yourself
With one square standing for five units, how tall is a bar for thirty?
Check your answer
Six squares tall.
Thirty divided by five is six.
Explain why bars keep equal widths
Choose the method: Ask what the eye compares when it reads a bar graph.
EZT practice question
Why keep bars the same width in a bar graph?
Show the worked solution
- A bar graph should show value through height alone.
- Different widths would make some bars look bigger for the same height.
- That misleads the eye.
Answer: Different widths would mislead the eye - only height should show the count.
Check: The answer protects the rule that height alone carries the value.
Watch for this: Do not treat width as decoration you can vary; it changes how big a bar looks.
Now try it yourself
Name two things a good graph needs.
Check your answer
A title and labelled axes.
Without them the reader cannot tell what the bars describe.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What is frequency?
Show answer and reason
How many times an item occurs in the data.
A frequency table lists items with these counts.
2. How do tally marks work?
Show answer and reason
One mark per item, grouped in bundles of five to count quickly.
The fifth line crosses the first four.
3. What is a pictograph?
Show answer and reason
A chart using pictures or symbols, each standing for a fixed number given in the key.
The key converts symbols into counts.
4. Why use equal widths in a bar graph?
Show answer and reason
So only the bar height shows the value.
Unequal widths mislead the eye.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Record the favourite fruit of ten friends and make a frequency table with tally marks.
- In a pictograph one book symbol stands for five books. How many books do seven and a half symbols show?
- Values six, nine, fifteen, twenty-one need a bar graph with eight squares of height - pick a scale.
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Questions about this practice page
- What is a pictograph?
- A chart that uses pictures or symbols, each standing for a fixed number, as given in the key.
- What is frequency?
- How many times an item occurs in the data.
- How do tally marks work?
- One mark per item, grouped in bundles of five so you can count quickly.
- Why use equal widths in a bar graph?
- So only the bar height shows the value - unequal widths mislead the eye.
- Are these the NCERT exercise questions for Data Handling and Presentation?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.