CBSE Class 6 Mathematics Data Handling and Presentation Worksheet Set 01

Short Answer Questions

Question 1. What is meant by data? Write any two examples of data that you could collect inside your own school.
Answer:
Data is any collection of facts, numbers, measures or observations that gives us information about something.
Example 1: the marks scored by every student of a class in a test.
Example 2: the number of students absent in each class on one day.
A plain list of answers is data too; it becomes useful once we organise it in a table.
In simple words: Data is any set of facts or numbers about things, like test marks or absentees.

Teacher's Note:
1. Accept any sensible school examples.
2. Stress that data must give information about something.

Question 2. Answer these questions about tally marks.
(i) In groups of how many are tally marks bunched, and how is the fifth mark drawn?
(ii) Describe how you would show the number 13 using tally marks.
Answer:
(i) Tally marks are bunched in groups of five. Four marks stand side by side and the fifth is drawn across these four, so a group of five is seen at a glance:
(ii) 13 = 5 + 5 + 3. So 13 is shown as two crossed groups of five followed by three single marks:
In simple words: Tally marks go in crossed fives; 13 is two crossed fives and three more strokes.

Teacher's Note:
1. Let children draw the marks themselves.
2. Counting by fives then ones gives the total fast.

Question 3. The number of pets kept by eight children is noted as: 2, 1, 3, 1, 2, 1, 4, 1.
(i) What is the frequency of the value 1?
(ii) In your own words, say what the word frequency means.
Answer:
(i) The value 1 appears 4 times, so its frequency is 4.
(ii) Frequency is the number of times a particular value or observation occurs in the data.
In simple words: 1 occurs four times, and frequency means how many times something occurs.

Teacher's Note:
1. Tick each 1 as you count it.
2. Do not confuse the value 1 with its frequency 4.

Question 4. In a pictograph, one glass symbol stands for 4 glasses of milk sold.
(i) How many glasses are shown by 7 symbols?
(ii) What number of glasses does half a symbol show?
Answer:
Key: one symbol = 4 glasses of milk.
(i) 7 symbols = 7 × 4 = 28 glasses.
(ii) Half a symbol = half of 4 = 2 glasses.
In simple words: Multiply symbols by 4; half a symbol is 2 glasses.

Teacher's Note:
1. Number of symbols × key gives the value.
2. A half symbol shows half the key.

Question 5. Write any three things that must appear on a bar graph so that another person can read it correctly. Give a short reason for each.
Answer:
(1) A title: it tells the reader what the graph is about.
(2) Labels on both axes: the names of the categories on one axis and the quantity counted on the other, so the reader knows what is being compared.
(3) The scale, such as 1 unit length = 5 students, with markings from zero in equal steps, so every bar length can be turned into a number.
In simple words: A bar graph needs a title, axis labels and a scale starting from zero.

Teacher's Note:
1. Ask: could a stranger read this graph?
2. Missing scale is the most common mistake.

Question 6. Write two differences between a pictograph and a bar graph.
Answer:
(1) A pictograph shows data by pictures or symbols, each standing for a fixed number given by the key. A bar graph shows data by bars of equal width whose heights show the values by a scale.
(2) A pictograph becomes hard when numbers are large or not multiples of the key, as part symbols are needed. A bar graph can show any number quickly, since the bar is just drawn to the right height.
In simple words: Pictographs use symbols and suit small neat numbers; bar graphs use bars and suit any numbers.

Teacher's Note:
1. Compare how each shows the value.
2. Compare how easy each is for large data.

Teacher's Note:
1. Strike off each name as you put its tally mark.
2. The total of the frequencies must equal 15.

Question 8. Why must the scale (key) always be written on a pictograph? Explain your answer with one short example.
Answer:
The key tells what one symbol stands for; without it the pictograph gives no numbers at all.
Example: 5 book symbols mean 5 books if the key is “1 symbol = 1 book”, but 50 books if the key is “1 symbol = 10 books”.
So the same picture could be read in many ways; the key removes this confusion.
In simple words: Without a key, the same symbols could mean 5 or 50, so the key is a must.

Teacher's Note:
1. Use one picture with two keys to show the point.
2. Always read the key first.

Teacher's Note:
1. ‘More than 3’ does not include 3.
2. Check that the frequencies add to 20.

Teacher's Note:
1. Find a number that divides all the values.
2. 10 would need half symbols for 35 and 25.

Question 11. In a bar graph the scale is 1 unit length = 6 water bottles.
(i) How many bottles does a bar of 7 unit lengths show?
(ii) How many unit lengths are needed to show 54 bottles?
Answer:
(i) 7 × 6 = 42 bottles.
(ii) 54 ÷ 6 = 9 unit lengths.
In simple words: Multiply units by 6 to get bottles; divide bottles by 6 to get units.

Teacher's Note:
1. Units to value: multiply. Value to units: divide.
2. Check: 9 × 6 = 54.

Question 12. In a bar graph, the bar for Hindi story books is 9 unit lengths long and stands for 45 books.
(i) Find the scale of this bar graph.
(ii) The bar for English story books is 6 unit lengths long. How many English story books are there?
Answer:
(i) 9 unit lengths = 45 books, so 1 unit length = 45 ÷ 9 = 5 books. The scale is 1 unit length = 5 books.
(ii) 6 × 5 = 30 English story books.
In simple words: Each unit is 5 books, so 6 units show 30 books.

Teacher's Note:
1. Scale = value ÷ length.
2. Use the scale for every other bar.

Teacher's Note:
1. Find the largest and smallest values first.
2. Graphs turn numbers into lengths.

Question 14. In a pictograph, one full symbol stands for 10 mangoes and half a symbol stands for 5 mangoes. Basket P shows 3 full symbols and one half symbol, and Basket Q shows 2 full symbols. Find the number of mangoes in each basket and the difference between them.
Answer:
Basket P: 3 × 10 + 5 = 35 mangoes.
Basket Q: 2 × 10 = 20 mangoes.
Difference = 35 − 20 = 15 mangoes.
In simple words: P has 35, Q has 20, so P has 15 more.

Teacher's Note:
1. Add the half symbol value separately.
2. Difference in symbols is 1.5, and 1.5 × 10 = 15 also works.

Question 15. A family’s monthly spending on six items varies from a smallest value of ₹400 to a largest value of ₹3400. The chart paper allows a bar of at most 18 unit lengths. Explain why the scale 1 unit length = ₹1 cannot be used, and suggest a suitable scale with a reason.
Answer:
With 1 unit length = ₹1, the ₹3400 bar would be 3400 unit lengths long, which cannot fit on chart paper.
A suitable scale is 1 unit length = ₹200.
Then the tallest bar is 3400 ÷ 200 = 17 unit lengths (within 18) and the shortest is 400 ÷ 200 = 2 unit lengths, still clearly visible.
In simple words: ₹1 per unit is far too long; ₹200 per unit gives bars from 2 to 17 units.

Teacher's Note:
1. Divide the largest value by the space allowed: 3400 ÷ 18 is about 189, so round up to a neat 200.
2. Check the smallest bar is still visible.

Teacher's Note:
1. Seven children reading 2 books each is 14 books, not 2.
2. Also check 3 + 5 + 7 + 4 + 1 = 20 children.

Question 17. On a shop poster, the sale of three brands of juice is shown by pictures of bottles. The bottle drawn for Brand C is not only taller than the other two but also much wider than them. Explain why such a picture can mislead a customer, and state how the picture should be drawn so that it is fair.
Answer:
Only one quantity, the number of bottles sold, is compared, so only one measurement of the picture should change.
When Brand C is drawn both taller and wider, its area becomes much larger than its true share. The eye compares the whole area, so Brand C looks far ahead even if it sold only a little more.
It also suggests a false idea that Brand C’s bottles are bigger.
Fair way: draw all three pictures (or bars) with the same width, let only the height change with the sales, keep equal gaps, and write the scale.
In simple words: Making a picture wider as well as taller exaggerates it; keep widths equal.

Teacher's Note:
1. The eye judges area, not just height.
2. Same width, equal gaps, clear scale.

Question 18. Rahul has data on the number of books in five cupboards, the largest number being 90. He draws the same data twice: once with the scale 1 unit length = 2 books and once with the scale 1 unit length = 20 books. Describe how the two bar graphs will look, and suggest a third scale that would suit a notebook page better than both of them. Give a reason.
Answer:
With 1 unit length = 2 books, the tallest bar is 90 ÷ 2 = 45 unit lengths, which will run off the page.
With 1 unit length = 20 books, the tallest bar is 90 ÷ 20 = 4.5 unit lengths. The graph is very small, and cupboards differing by 10 books differ by only half a unit, so differences are hard to see.
Better: 1 unit length = 10 books. The tallest bar is 90 ÷ 10 = 9 unit lengths, which fits the page and still shows differences clearly.
In simple words: 2 books per unit is too tall, 20 is too small; 10 books per unit fits well.

Teacher's Note:
1. A good scale gives a tallest bar of about 8 to 15 units.
2. Neat numbers like 10 make reading easy.

Question 19. Give a reason for each choice below.
(i) Would you use vertical bars or horizontal bars to show the heights of five tall buildings?
(ii) Would you use vertical bars or horizontal bars to show the lengths of five rivers?
Answer:
(i) Vertical bars. Height is measured upwards from the ground, so upward bars look natural and compare like the buildings themselves.
(ii) Horizontal bars. A river’s length runs along the ground, so flat bars suggest length and make the comparison easy to picture.
In simple words: Upright bars for heights, flat bars for lengths along the ground.

Teacher's Note:
1. Both ways are correct graphs; this is about looking natural.
2. Think of how the real object lies.

Question 20. Rohit wants to find out which month is the most common birthday month among the 600 students of his school. Describe the steps he should follow to collect and organise this data, and say which way of presenting it he should choose at the end. Give a reason for your choice.
Answer:
Collect: go class by class and note only the birth month of every student (or ask class teachers to read it from the register), so no one is missed.
Organise: make a table with twelve rows, one per month, and put a tally mark against a month each time it is named, grouping the marks in fives.
Count: write the frequency beside each month and check that the twelve frequencies add up to 600.
Present: a bar graph is better. The frequencies are large and will not be neat multiples of any key, so a pictograph would need many part symbols; with a scale such as 1 unit length = 10 students, the tallest bar shows the most common month at a glance.
In simple words: Collect months, tally them, count, and show them as a bar graph.

Teacher's Note:
1. The check total of 600 catches mistakes.
2. Large, uneven numbers suit a bar graph.