CBSE Class 6 Mathematics Data Handling and Presentation Assignment Set 01

Very Short Answer Questions

Question 1. Write in one sentence what is meant by data.
Answer:
Data is any collection of facts, numbers, measures or observations that gives us information about things.

Teacher's Note:
1. Give an example: the heights of your classmates.
2. Data can be words as well as numbers.

Question 2. Give two examples of data that you can collect inside your own classroom.
Answer:
(1) The favourite game of each classmate.
(2) The height (or shoe size) of each classmate.

Teacher's Note:
1. Any fact you can note for every student is data.
2. Let children suggest their own examples.

Question 3. What is a tally mark used for?
Answer:
A tally mark is a short stroke put down for each item while the data is being counted, so the counting can go on without going back to the start.

Teacher's Note:
1. One stroke for one item.
2. Tally marks help us count as the data comes in.

Question 4. Why are tally marks made in groups of five?
Answer:
Groups of five can be counted very quickly, so finding the frequency becomes easy.
Example: = 5.

Teacher's Note:
1. Counting in fives is faster than counting ones.
2. The fifth stroke closes the group.

Question 5. The frequency of hockey in a table is 12. How many complete groups of five tally marks will be drawn for hockey, and how many single marks will be left over?
Answer:
12 = 2 × 5 + 2.
So 2 complete groups and 2 single marks are drawn:

Teacher's Note:
1. Divide by 5: the quotient gives groups, the remainder gives single marks.
2. Check: 5 + 5 + 2 = 12.

Question 6. What is meant by the frequency of a value in data?
Answer:
The frequency of a value is the number of times that value occurs in the data.

Teacher's Note:
1. Frequency answers ‘how many times?’.
2. All frequencies add up to the total number of items.

Question 7. How does a pictograph show data?
Answer:
A pictograph shows data by pictures or symbols; each symbol stands for a fixed number of items given by its key.

Teacher's Note:
1. No numbers are written for the categories.
2. The key gives the value of one symbol.

Question 8. Why can a pictograph not be read properly if its key is missing?
Answer:
Without the key we do not know how many items one symbol stands for, so the numbers behind the picture cannot be found.

Teacher's Note:
1. The same picture could mean 5 or 50 items.
2. A key is a must on every pictograph.

Question 9. In a bar graph, what does the height of a bar tell us?
Answer:
The height of a bar tells the value (frequency or quantity) of the category written below it.

Teacher's Note:
1. Read the height against the scale on the vertical line.
2. Taller bar, bigger value.

Question 10. Why is the width of every bar kept the same in a bar graph?
Answer:
So that only the lengths differ; then categories are compared by length alone and the picture does not mislead.

Teacher's Note:
1. A wider bar would look bigger than it is.
2. Width carries no number.

Question 11. What is meant by the scale of a bar graph?
Answer:
The scale tells how many items one unit length of a bar stands for, for example 1 unit length = 100 vehicles.

Teacher's Note:
1. The scale is written on the graph.
2. Its markings start from zero.

Question 12. Name the two ways in which the bars of a bar graph may be drawn.
Answer:
The bars may be drawn vertically (a column graph) or horizontally.

Teacher's Note:
1. Vertical bars stand up; horizontal bars lie flat.
2. Both show the same data.

Question 13. Name the three columns you would make in a frequency table of the favourite sweets of your class.
Answer:
Sweet (name of the sweet), Tally Marks, and Frequency (number of students who chose it).

Teacher's Note:
1. Category, tally marks, frequency is the usual order.
2. The frequency column is filled after counting.

Question 14. Write one reason why a bar graph can be read faster than a frequency table.
Answer:
A bar graph shows all categories side by side, so the biggest, the smallest and the differences are seen at one glance without reading numbers.

Teacher's Note:
1. Eyes compare lengths faster than numbers.
2. That is why graphs are used in news reports.

Question 15. In a bar graph showing the number of students absent in each class, the bar for Class V has no height at all. What does this tell you?
Answer:
It means no student of Class V was absent; Class V had full attendance.

Teacher's Note:
1. A bar of no height stands for zero.
2. Zero is a value too, not missing data.

Question 16. In a pictograph, one symbol stands for 4 girls. How many girls are shown by 6 symbols?
Answer:
6 × 4 = 24 girls.

Teacher's Note:
1. Number of symbols × key.
2. Check: 4 + 4 + 4 + 4 + 4 + 4 = 24.

Question 17. In a pictograph, one symbol stands for 10 books. How many symbols are needed to show 35 books?
Answer:
3 full symbols show 30 books and a half symbol shows 5 more.
So 3 full symbols and 1 half symbol are needed.

Teacher's Note:
1. 35 ÷ 10 = 3 and a half.
2. Half a symbol stands for half the key.

Question 18. The key of a pictograph is “one symbol = 10 students”. Why is it difficult to show 27 students on this pictograph?
Answer:
27 is not a multiple of 10 (nor of 5). Two symbols give 20, but the remaining 7 students cannot be shown neatly by a part of a symbol.

Teacher's Note:
1. Parts like seven-tenths of a symbol are hard to draw.
2. A key of 1 or 3 would suit 27 better.

Question 19. The scale of a bar graph is 1 unit length = 5 saplings. How many units long will the bar for 35 saplings be?
Answer:
35 ÷ 5 = 7 units.

Teacher's Note:
1. Length = value ÷ scale.
2. Check: 7 × 5 = 35.

Question 20. Two bars of a bar graph are 4 units and 6 units long and the scale is 1 unit length = 20 books. How many more books does the longer bar show?
Answer:
The bars differ by 6 − 4 = 2 units.
2 × 20 = 40 more books.

Teacher's Note:
1. Subtract units first, then multiply by the scale.
2. Check: 120 − 80 = 40.

Question 21. Arrange the shoe sizes 5, 4, 6, 4, 5, 7, 4 in ascending order and state how many children wear size 4.
Answer:
Ascending order: 4, 4, 4, 5, 5, 6, 7.
3 children wear size 4.

Teacher's Note:
1. Ascending means smallest to largest.
2. After sorting, equal values sit together and are easy to count.

Question 22. Why must a suitable scale be chosen before a bar graph is drawn?
Answer:
So that the longest bar fits in the space available and the bars are still long enough to compare easily.

Teacher's Note:
1. Look at the largest value first.
2. Too big a scale makes tiny bars; too small a scale makes bars run off the page.

Question 23. Which two lines are drawn first while making a bar graph, and what is marked along each of them?
Answer:
A horizontal line and a vertical line, perpendicular to each other.
The categories are marked at equal gaps on the horizontal line; the frequencies, starting from zero, on the vertical line.

Teacher's Note:
1. Categories go across, numbers go up.
2. Start the numbers at zero.

Question 24. What are infographics?
Answer:
Infographics are data pictures, such as bar graphs, made more attractive with extra images, shapes and colours so that the information catches the eye.

Teacher's Note:
1. They look nice but can mislead.
2. Always check the numbers behind them.

Question 25. A chart is to show the heights of five trees of a park. Would you draw the bars vertically or horizontally? Give one reason.
Answer:
Vertically. The height of a tree is measured upwards from the ground, so upright bars show it naturally.

Teacher's Note:
1. Match the bar direction to the real thing.
2. Lengths along the ground suit horizontal bars.

Question 26. A bowler took 0 wickets in 2 matches, 1 wicket in 4 matches, 2 wickets in 6 matches and 3 wickets in 8 matches. Find the total number of wickets he took in these matches.
Answer:
Multiply each number of wickets by its matches and add:
0 × 2 + 1 × 4 + 2 × 6 + 3 × 8 = 0 + 4 + 12 + 24 = 40 wickets.

Teacher's Note:
1. Do not just add 0 + 1 + 2 + 3.
2. Each value counts as many times as it happened.

Question 27. The marks of three students are 88, 90 and 92. Their bar graph is drawn with the vertical scale beginning at 85. Why can this graph mislead a reader?
Answer:
Starting at 85, the bars show only 3, 5 and 7 instead of 88, 90 and 92.
So the bar for 92 looks more than twice the bar for 88, though the marks differ by only 4.

Teacher's Note:
1. The scale must start at zero.
2. Small differences get blown up otherwise.

Question 28. In an infographic of mountains, the taller mountains are drawn as wider triangles. What wrong idea can this give the reader?
Answer:
It suggests that a taller mountain is also wider, which the height data never said.

Teacher's Note:
1. Only the height should change.
2. Extra width adds false information.

Question 29. Two villages have 15 and 45 dogs. Suggest a suitable key for a pictograph of this data and write how many symbols each village will need.
Answer:
Key: one symbol = 5 dogs.
First village: 15 ÷ 5 = 3 symbols; second village: 45 ÷ 5 = 9 symbols.

Teacher's Note:
1. Pick a key that divides every number exactly.
2. A key of 15 would also work: 1 and 3 symbols.

Question 30. A shop sold 240, 260, 250 and 270 shirts in four months. Which scale would you choose for its bar graph, and how will the four bars look?
Answer:
Take 1 unit length = 10 shirts, with the scale starting at 0. The bars are 24, 26, 25 and 27 units.
The four bars will look almost equally tall, which is right, since the sales were nearly the same.

Teacher's Note:
1. An honest graph shows nearly equal data as nearly equal bars.
2. Do not start the scale at 240 to make it look dramatic.