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Class 6 Maths: Data Handling and Presentation, 8 practice questions with answers

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These are 8 practice questions on Class 6 Maths Chapter 4, Data Handling and Presentation, of the new NCERT textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover why the fifth tally mark crosses the other four, frequency, the column graph, changing the scale of a bar graph, the key of a pictograph, comparing graphs drawn to different scales, a scale that does not start at zero, and pictures that can mislead. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-computed by a test script and checked against the textbook page it cites, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash: Textbook of Mathematics for Grade 6, Chapter 4, printed pages 74 to 106):

Collecting and organising data

Question 1. When Arjun keeps a tally, he draws one upright mark for each vote, but for the fifth vote he draws a line across the four marks instead of a fifth upright mark. Why does the tally method do this, and how does it help when he counts the total?

Answer: the crossing line closes off a bundle of five, so the marks can be counted in fives instead of one by one. In the chapter's method, a mark is made for each item, and when the count reaches 5, a line is drawn through the previous four. Each crossed group then always means 5, so at the end you count the groups in fives and add the few single marks left over, which is quicker and less likely to go wrong than counting a long row of strokes. (The chapter shows the method; the reason is our explanation.) (Tally marks, page 76.)

Question 2. In a table, the row for 'mango' says 11, because 11 children chose mango. What is the number 11 called?

Answer: the frequency of mango. The number of times a category occurs in the data, here the number of children who chose mango, is called its frequency. (Frequency, page 77.)

Pictographs and bar graphs

Question 3. In the chapter, the heights of the tallest mountains are first drawn with bars lying flat, and then the graph is turned so that the bars stand upright. (a) What is a bar graph with upright bars also called? (b) Why does the chapter turn the mountain graph upright?

Answer: (a) a column graph; (b) the bars stand for heights, and upright bars grow up from the ground like mountains, so the heights are easier to picture and compare. The chapter says that because the boxes show heights, it is better and more pleasing to the eye to rotate the picture so that they rise from the ground. Such a graph is also named a column graph, after the pillars, or columns, that hold up the roof of a building. (Column graphs, page 102.)

Question 4. A bar graph of the number of passengers on a ferry each day uses the scale 1 unit length = 50 passengers. Neha redraws it with the scale 1 unit length = 25 passengers. (a) What happens to the length of every bar? (b) A bar was 6 units long in the first graph. How long is it in Neha's graph?

Answer: (a) every bar becomes twice as long; (b) 12 units. In Neha's graph each unit stands for half as many passengers, so a bar needs twice as many units to show the same number. The 6-unit bar shows 6 × 50 = 300 passengers, and 300 ÷ 25 = 12 units. Her graph will also need twice the height of paper, which is why the scale is chosen so that the graph fits. (Bar graphs and scales, page 87, and the key points on page 100.)

Question 5. A pictograph of birds counted at a lake has no key. Rahul says the row with 4 symbols shows 4 birds. Why can't he be sure?

Answer: without a key, one symbol could stand for 1 bird or for many. In a pictograph, each picture can stand for one unit or for more than one, so a scale or key must be given to show what one symbol means. If one symbol stood for 5 birds, the row would show 4 × 5 = 20 birds. (The key of a pictograph, pages 83 and 106.)

Reading graphs carefully

Question 6. Two chess clubs each drew a bar graph of how many members said 'Yes' to a new timetable. Club P's graph uses 1 unit length = 20 members; Club Q's graph uses 1 unit length = 50 members. Both 'Yes' bars are 3 units long. Moti says both clubs had the same number of 'Yes' answers. Is he right?

Answer: no; Club P had 60 'Yes' answers and Club Q had 150. The bars are the same length, but the units stand for different numbers: 3 × 20 = 60 for Club P and 3 × 50 = 150 for Club Q, so Club Q had 150 − 60 = 90 more. Bars can be compared by length only when the graphs use the same scale, which is why the chapter says the scale of a bar graph must be stated. (Scales, page 100; the summary, page 106.)

Question 7. Riya draws a bar graph of votes: 62 for one team and 66 for the other, with 1 unit length = 1 vote. Her vertical scale starts at 58 instead of 0. (a) How many units tall is each bar above her starting line? (b) Which rule from the chapter has she broken, and how tall would the bars be if she followed it, with the same scale?

Answer: (a) 4 units and 8 units; (b) the markings of the scale must start from zero; the bars would be 62 and 66 units tall. Starting at 58, the bars rise 62 − 58 = 4 and 66 − 58 = 8 units, so the second bar looks twice as tall as the first, although 66 is only 4 votes more than 62. If the markings start from zero, as the chapter says they must, the bars are 62 and 66 units tall and look nearly equal, as they should. (The scale must start from zero, key points on page 100.)

Question 8. A poster shows tea sales doubling by drawing this year's teacup twice as tall and twice as wide as last year's. About how many times the space does the new cup take, and how should it be drawn?

Answer: about 2 × 2 = 4 times the space; keep the width the same and double only the height. Doubling both the height and the width makes the cup cover about four times the space, so sales look as if they grew four times, not two. Like the equal-width bars of a bar graph, the cup should keep the same width and grow only in height. Pictures made wider as well as taller can suggest information that is not in the data. (Infographics, page 104.)

Questions students ask

What is the difference between a pictograph and a bar graph? A pictograph shows each number with pictures, using a key for what one picture stands for. A bar graph shows each number with the length or height of a bar, using a scale; it is easier to draw when the numbers are large. (Pages 80, 83 and 85.)

What is a scale in a bar graph? It tells how much one unit of length stands for, for example 1 unit length = 10 runs. It is chosen from the smallest and largest numbers in the data, so that the graph fits on the page. (Pages 90 and 100.)

What is an infographic? A data picture, such as a bar graph, decorated with more artistic images to catch the eye. It can communicate quickly, but it should not add shapes or sizes that suggest information that is not in the data. (Pages 103 and 104.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 73.

The facts are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Data Handling and Presentation, Class 6 worksheet. Printable, in English, Hindi and Marathi, with an answer key.