CBSE Class 6 Mathematics Data Handling and Presentation MCQs Set 11

Answer: (b) Any collection of facts, numbers, measures or observations that gives information about things

Explanation:
1. Data is any collection of facts, numbers, measures or observations that tells us something about things.
2. A list of favourite colours or the weights of all children of a class are both data.
3. So the answer is option (b).

Teacher's Note:
1. Data need not be only numbers; names and colours are data too.
2. Remember: data always gives information about something.

Answer: (a) As a line drawn across the first four marks

Explanation:
1. Tally marks are bunched in groups of five.
2. Four marks stand side by side and the fifth is drawn across the first four.
3. This lets us count each group of five in one look.

Teacher's Note:
1. Show the class a crossed group on the board: .
2. Counting in fives is faster than counting one by one.

Answer: (c) the frequency of gulab jamun

Explanation:
1. The number written against a category tells how many times it was chosen.
2. This count is called its frequency.
3. So 9 is the frequency of gulab jamun.

Teacher's Note:
1. Frequency = how many times.
2. Tally marks are strokes; the frequency is the number they add up to.

Answer: (b) what one symbol of the pictograph stands for

Explanation:
1. This note is the key (or scale) of the pictograph.
2. It tells us that every symbol drawn stands for 5 students.
3. So it tells what one symbol stands for.

Teacher's Note:
1. Always read the key before reading a pictograph.
2. The key does not give the total; we must count symbols for that.

Answer: (d) the same width

Explanation:
1. In a bar graph only the length (height) of a bar shows the value.
2. So every bar is drawn with the same width, and categories are compared by length alone.

Teacher's Note:
1. Heights change, widths stay the same.
2. Equal gaps are also left between the bars.

Answer: (b) 6

Explanation:
1. The scale is 1 unit length = 1 book.
2. The top of Dia’s bar is level with the line marked 6.
3. So Dia read 6 story books.

Teacher's Note:
1. Move your eye straight across from the top of the bar to the vertical axis.
2. Do not mix up Dia’s bar with Eshan’s bar next to it.

Answer: (c) 13

Explanation:
1. Each complete group stands for 5.
2. 2 groups give 2 × 5 = 10, and 3 more marks make 10 + 3 = 13.

Teacher's Note:
1. Count the crossed groups in fives first, then add the single marks.
2. The marks look like this: .

Answer: (d) Both the statements are true

Explanation:
1. A pictograph does show data by pictures or symbols, so Statement I is true.
2. Without the key we cannot know how many items one symbol stands for, so Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Check each statement on its own.
2. The key is the most important part of a pictograph.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A plain list has to be read name by name, so A is true.
2. Organising the data into a frequency table lets us compare games easily, so R is true.
3. R tells exactly why the list did not help, so R explains A.

Teacher's Note:
1. Raw data must be organised before it is useful.
2. Ask: does R give the reason for A? Here it does.

Answer: (a) (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r)

Explanation:
1. A tally mark is a short stroke used while counting: (i)-(q).
2. Frequency is the number of times a value occurs: (ii)-(s).
3. The key tells what one symbol stands for: (iii)-(p); the length of a bar shows the value: (iv)-(r).
4. So the answer is (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r).

Teacher's Note:
1. Match the pair you are surest about first.
2. Then pick the option that contains all your pairs.

Answer: (c) zero

Explanation:
1. The markings of the scale of a bar graph must start from zero.
2. If they start anywhere else, the lengths of the bars no longer show the true values.

Teacher's Note:
1. Zero at the bottom keeps the bar lengths honest.
2. Starting higher makes small differences look large.

Answer: (b) column graph

Explanation:
1. Vertical bars stand up like the columns (pillars) of a building.
2. So such a bar graph is called a column graph.

Teacher's Note:
1. Columns stand up; rows lie flat.
2. Heights of mountains or trees suit a column graph.

Answer: (a) half of the number shown by one full symbol

Explanation:
1. A part of a symbol stands for the same part of the key.
2. If a full symbol stands for 10 children, half a symbol stands for 5 children.
3. So half a symbol shows half of the number shown by one full symbol.

Teacher's Note:
1. Half the picture means half the number.
2. Try it with a key of 4: half a symbol is 2.

Answer: (c) 45

Explanation:
1. 4 full symbols stand for 4 × 10 = 40 books.
2. The half symbol stands for half of 10, that is 5 books.
3. Total = 40 + 5 = 45 books.

Teacher's Note:
1. A half symbol is not 1; it is half the key.
2. Option 41 is the common mistake.

Answer: (b) 30

Explanation:
1. The key is: one symbol = 10 eggs.
2. Thursday has 5 full symbols, that is 5 × 10 = 50 eggs; Wednesday has 2 full symbols, that is 2 × 10 = 20 eggs.
3. Difference = 50 − 20 = 30 eggs.

Teacher's Note:
1. 3 is only the difference in symbols; multiply it by the key.
2. Always use the key before subtracting.

Answer: (d) A is false, but R is true.

Explanation:
1. One symbol may stand for 5, 10 or any fixed number of objects, so A is false.
2. The key is chosen to suit the size of the data, so R is true.
3. So A is false but R is true.

Teacher's Note:
1. The word ‘always’ makes A wrong.
2. A big key saves time and space when numbers are large.

Answer: (a) Both the statements are true

Explanation:
1. Drawing many symbols for large numbers is slow, so a bar graph is easier: Statement I is true.
2. The scale is fixed by looking at the smallest and largest values so the graph fits the paper: Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Large data suits bar graphs.
2. The largest value decides how tall the graph will be.

Answer: (c) 150 litres

Explanation:
1. Each unit length stands for 25 litres.
2. 6 units stand for 6 × 25 = 150 litres.

Teacher's Note:
1. Value = number of units × scale.
2. Do not add 6 to 125; multiply.

Answer: (b) (i)-(s), (ii)-(p), (iii)-(r), (iv)-(q)

Explanation:
1. Height = amount ÷ 200.
2. 600 ÷ 200 = 3 units (s); 1000 ÷ 200 = 5 units (p).
3. 1600 ÷ 200 = 8 units (r); 400 ÷ 200 = 2 units (q).
4. So the answer is (i)-(s), (ii)-(p), (iii)-(r), (iv)-(q).

Teacher's Note:
1. Divide each amount by the scale.
2. Check one pair, e.g. 400 → 2 units, to rule out options fast.

Answer: (d) 40

Explanation:
1. The February bar reaches 70 cycles.
2. The April bar reaches 30 cycles.
3. Difference = 70 − 30 = 40 cycles.

Teacher's Note:
1. Read both bars first, then subtract.
2. 70 is February alone and 100 is the sum; both are traps.

Answer: (a) the bars are free standing and stand for separate categories

Explanation:
1. The equal gaps show that every bar stands on its own.
2. Each bar stands for a separate category; the gaps carry no value.
3. So the answer is option (a).

Teacher's Note:
1. Gaps separate the categories.
2. The gap size never shows any number.

Answer: (c) A is true, but R is false.

Explanation:
1. Equal gaps are always left between bars, so A is true.
2. The frequency is shown by the length or height of a bar, not by its width, which is the same for all bars. So R is false.
3. So A is true but R is false.

Teacher's Note:
1. Width is fixed; height carries the number.
2. Always test R on its own first.

Answer: (b) 100 mm

Explanation:
1. Reading the bars: Monday 15 mm, Tuesday 25 mm, Wednesday 10 mm, Thursday 20 mm, Friday 30 mm.
2. Total = 15 + 25 + 10 + 20 + 30 = 100 mm.

Teacher's Note:
1. Write each bar’s value before adding.
2. Group easy pairs: 15 + 25 = 40 and 10 + 20 + 30 = 60.

Answer: (d) Only Statement II is true

Explanation:
1. Adding only 0, 1, 2, 3, … ignores how many matches each happened in, so Statement I is false.
2. Each number of wickets must be multiplied by its number of matches and the products added, so Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. A value that happens 4 times must be counted 4 times.
2. Multiply, then add.

Answer: (c) A is true, but R is false.

Explanation:
1. When the scale starts at 60, only the part above 60 is drawn, so tiny differences look huge: A is true.
2. The data values themselves do not change at all; only the picture becomes misleading. So R is false.
3. So A is true but R is false.

Teacher's Note:
1. The picture changes, the numbers do not.
2. This is a common trick in advertisements.

Answer: (d) Only Statements I and II are true

Explanation:
1. Bars may be horizontal or vertical, so Statement I is true.
2. Heights rise upward from the ground, so vertical bars suit them: Statement II is true.
3. Every bar must have the same width, so Statement III is false.
4. So only Statements I and II are true.

Teacher's Note:
1. Widths are never changed in a bar graph.
2. Upward things suit upright bars.

Answer: (a) The numbers on the vertical line do not start from zero

Explanation:
1. The vertical line starts at 90, not at 0, so only the marks above 90 are drawn.
2. Ravi’s bar shows 92 − 90 = 2 and Tarun’s shows 98 − 90 = 8, which looks like four times as much.
3. So the cause is that the numbers on the vertical line do not start from zero.

Teacher's Note:
1. Look at the bottom number of the vertical axis first.
2. The widths and gaps here are all equal, so (b) and (c) are wrong.

Answer: (c) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. 0 to 7 children is small data: 1 unit length = 1 child (r).
2. 150 to 600 litres fits 1 unit length = 50 litres (s): bars of 3 to 12 units.
3. 10 to 70 saplings fits 1 unit length = 10 saplings (p); Rs 400 to Rs 3600 fits 1 unit length = Rs 400 (q).
4. So the answer is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. The units must match: children with child, litres with litres.
2. That alone fixes every pair.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. 27 is not a multiple of 10, so the part of a symbol for 7 students cannot be drawn neatly: A is true.
2. A pictograph does present data through pictures, so R is true.
3. But R does not say why 27 is hard to show; the real reason is that 27 is not a multiple of 10. So R is not the correct explanation.

Teacher's Note:
1. Both can be true and still not be linked.
2. The real difficulty is the leftover 7.

Answer: (d) A is false, but R is true.

Explanation:
1. Looking attractive does not make a picture accurate, so A is false.
2. Extra details, such as wider shapes for taller bars, can suggest things the data never said, so R is true.
3. So A is false but R is true.

Teacher's Note:
1. Pretty is not the same as correct.
2. Read infographics with care.