Start with the meaning
NCERT connection: Grade 6 Ganita Prakash, “Data Handling and Presentation”. These are independent BananaLearn notes and original practice, not official NCERT material or a complete set of textbook exercise solutions. Match the chapter name to the book used by your school. You need whole-number counting, addition and subtraction. The focus here is categorical data, tally marks and bar graphs, not averages or probability.
Begin with a clear question
Suppose a group of children each chooses one favourite activity. The categories might be reading, drawing and cycling. Count each response once and keep a category for every allowed response.
A frequency is the number of times a category occurs. It is not the category name and it is not a ranking. If seven children choose drawing, the frequency for drawing is seven.
Use tallies to avoid losing count
Record four individual strokes and use a fifth crossing stroke to make a group of five. Two full groups and three extra strokes represent thirteen responses. Count groups first, then the extras.
Check that the total frequency equals the number of responses collected. If it does not, look for a missing response, a repeated response or an unclear category before drawing a graph.
Read the scale before the bar
On the graph in this guide, each vertical interval represents two children. The reading bar reaches eight, drawing reaches twelve and cycling reaches six. The label gives the unit: children.
Use equal-width bars, equal gaps and a consistent scale starting at zero for these comparisons. A bar halfway between ten and twelve represents eleven; it does not have to end on a labelled tick.
Answer only what the survey supports
The difference between twelve and eight is four children. The total for all three categories is twenty-six. State whether your answer is a difference, a total or a category.
This group choosing drawing most often does not prove that every child everywhere prefers drawing. A graph describes the responses collected. Check who was asked and whether each child could select more than one category before interpreting a total.
Worked examples, step by step
Example 1: Read the illustrated graph
- Read the axis: number of children, with two children per interval.
- Reading reaches 8, drawing reaches 12 and cycling reaches 6.
- Drawing has four more responses than reading because 12 − 8 = 4.
Example 2: Convert a short list into frequencies
- For red, blue, red, green, blue, red, make one category for each colour.
- Count red three times, blue twice and green once.
- The frequencies total 3 + 2 + 1 = 6, matching the six responses.
Example 3: Choose a sensible scale
- A survey has category counts 10, 15 and 20. Start a vertical axis at zero.
- Intervals of five reach 20 in four equal steps.
- Label 0, 5, 10, 15, 20; do not mix different interval sizes to fit individual bars.
Common mistakes and useful repairs
Counting tick marks instead of intervals
A bar at the fourth interval on a scale of two represents eight, not four. Read two consecutive tick labels to identify the step.
Adding categories that overlap as if they were separate children
If a child can choose two activities, the sum counts selections. It may exceed the number of children. Check the collection rule.
Try before revealing
Quick understanding check
Read the check answers
20. Each interval adds five; four intervals give 4 × 5 = 20.
Whether responses can overlap. Overlapping choices can make the total count selections rather than distinct people.
Grade 6 data handling: tally marks and bar graph questions — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
In the illustrated graph, how many children chose drawing?
Show answer and reasoning
12 children. The drawing bar reaches 12 on the vertical scale.
How many more chose reading than cycling?
Show answer and reasoning
2 children. Reading is 8 and cycling is 6, so 8 − 6 = 2.
How many responses are shown altogether?
Show answer and reasoning
26 responses. Add 8 + 12 + 6.
A tally has three groups of five and two extra strokes. What is its frequency?
Show answer and reasoning
17. 3 × 5 + 2 = 17.
A bar reaches the fifth interval on an axis with three items per interval. What count does it show?
Show answer and reasoning
15 items. 5 × 3 = 15, assuming the axis starts at zero.
Counts for cats, dogs and fish are 9, 6 and 5. What is the total?
Show answer and reasoning
20 responses. 9 + 6 + 5 = 20.
For the counts 9, 6 and 5, how many more cats than fish are recorded?
Show answer and reasoning
4. 9 − 5 = 4.
Twenty children each make two selections. Must the frequency total equal twenty?
Show answer and reasoning
No; it equals 40 selections if every child makes exactly two. A selection total and a count of distinct children are different quantities.
Grade 6 data handling: tally marks and bar graph questions — worked answer key
12 children. The drawing bar reaches 12 on the vertical scale.
2 children. Reading is 8 and cycling is 6, so 8 − 6 = 2.
26 responses. Add 8 + 12 + 6.
17. 3 × 5 + 2 = 17.
15 items. 5 × 3 = 15, assuming the axis starts at zero.
20 responses. 9 + 6 + 5 = 20.
4. 9 − 5 = 4.
No; it equals 40 selections if every child makes exactly two. A selection total and a count of distinct children are different quantities.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, compare the closest worked example with your own drawing before trying a fresh problem.
Help at home: Collect a tiny survey
Ask each family member to choose exactly one of three fruits. Let your child create a frequency list, check its total and draw a bar graph with a labelled scale.
Ask “What can we say about this family?” followed by “Can we say that about the whole school?” This makes the limits of a small survey visible without adding statistical jargon.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Are these NCERT exercise solutions?
No. These are original questions with worked answers that support the named topic. Use the official textbook link for the book itself. Exercise numbers and school sequences can differ between editions.
How should a parent use the practice?
Ask for one independent attempt before revealing an answer. Notice whether the difficulty is reading the question, representing the idea or calculating. Revisit the matching example, then try a fresh question rather than copying the worked answer.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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