NCERT MCQ Solutions for Class 6 Maths Chapter 4 Data Handling and Presentation

A list of favourite colours records information about the students. Data can consist of facts, numbers, measurements, observations or descriptions. It does not have to contain numbers; the recorded colour choices also form data.

The most popular TV show depends on the choices of the classmates. Their responses must be collected and counted. The other questions ask for fixed facts, so a survey of classmates is not needed to answer them.

Each complete tally group represents 5 students.
Frequency = 5 + 5 + 3
= 13
The extra three marks are counted in addition to the two groups. Thus, 13 students chose that sweet.

The table records the number of students in each category, not their names.
Total choosing the two sweets = 6 + 9 = 15.
Although the totals can be compared, a particular student cannot be matched to a sweet without additional information.

Sizes larger than 4 are 5, 6 and 7.
Number of students = 10 + 4 + 1
= 15
The students wearing sizes 3 and 4 are excluded because their sizes are not larger than 4.

The first step in organizing data is collecting the data.

In a pictograph, each symbol represents A scale or quantity.

Two complete symbols represent 2 × 10 = 20 children.
A half-symbol represents 10 ÷ 2 = 5 children.
Total = 20 + 5 = 25 children.
The half-symbol must be included when reading the pictograph.

Full attendance means that no student is absent. The fifth entry, corresponding to Class V, is 0. Therefore, Class V had full attendance. The other classes each have at least one absent student.

Number of symbols = Number of students ÷ Students per symbol
= 35 ÷ 5
= 7
Since 35 is exactly divisible by 5, seven complete symbols represent the class and no part-symbol is needed.

450 = 400 + 50
400 kites need 4 complete symbols.
50 kites need half of a 100-kite symbol.
Therefore, four complete symbols and one half-symbol show 450 kites accurately without rounding the number.

Complete and half-symbols represent groups of 10 and 5. Any total made from them is a multiple of 5.
33 = 30 + 3
The remaining 3 students cannot be represented by either of the allowed symbols.

Ascending order is used to arrange numbers from smallest to largest.

The largest shoe size recorded in the example is 7.

In a bar graph, the height or length of each bar shows the quantity. Keeping the widths equal and the gaps uniform makes the comparison clear. The heights need not be equal because different categories can have different frequencies.

Population = Bar length × Population per unit
= 8 × 10 crore
= 80 crore
The scale tells us the value of each unit, so the bar length must be multiplied by 10, not read as 8 crore.

A longer bar represents a larger vehicle count. Among 150, 1200, 1000, 800, 700 and 600, the largest number is 1200. It belongs to the 7–8 interval, so that interval has the longest bar.

Total vehicles = 150 + 1200 + 1000 + 800 + 700 + 600
= 4450
Each count belongs to a different hourly interval, so all six counts are added. Since the counts are approximate, the total is also approximate.

Bar height = Frequency ÷ Students per unit
= 13 ÷ 1
= 13 units
Every unit of height represents one student. A 13-unit bar therefore shows the 13 students who prefer gujiya.

A bar graph of uniform width bars uses to represent data.

The primary purpose of collecting data is to convey information.

The sixth score in the list is 0.
Bar height = 0 ÷ Scale value = 0.
Thus, the bar stays at the baseline. Here the zero is a recorded score, not a missing value.

One-fourth of the food expense = ₹3400 ÷ 4 = ₹850
Difference = ₹850 − ₹800 = ₹50
Therefore, the education expense is ₹50 less than one-fourth of the food expense.

Bar height = Expense ÷ Amount per unit
= 800 ÷ 200
= 4 units
Checking the scale, 4 × ₹200 = ₹800. Therefore, a four-unit bar represents the education expense correctly.

Tickets per unit = Total tickets ÷ Bar height
= 24 ÷ 6
= 4
Therefore, one unit length represents 4 tickets. This same scale must be used for all the other bars in the graph.

Bar height = Number of tickets ÷ Tickets per unit
= 28 ÷ 4
= 7 units
A bar of 6 units would show only 24 tickets. The correct bar must reach 7 units to represent all 28 tickets.

Bar graph is suitable for large data sets.

1-unit length represents 10 vehicles
So, a bar of height 6 units = 6 x 10 = 60 vehicles.

Total wickets = (0 × 2) + (1 × 4) + (2 × 6) + (3 × 8) + (4 × 3) + (5 × 5) + (6 × 1) + (7 × 1)
= 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7
= 90
Each wicket count is multiplied by the number of matches with that count.

All four listed groups meet the condition “at least 4 wickets”.
Number of matches = 3 + 5 + 1 + 1
= 10
The frequencies of the matches are added, not the wicket counts 4, 5, 6 and 7.

Number of symbols = 36 ÷ 6
= 6
Each symbol stands for six dogs, so six symbols represent 6 × 6 = 36 dogs. No half-symbol is needed because 36 is a multiple of 6.

Dogs in B and D = 36 + 48 = 84
Dogs in A, C, E and F = 18 + 12 + 18 + 24 = 72
Difference = 84 − 72 = 12
Thus, B and D together have 12 more dogs than the other four villages together.

After excluding playing, the frequencies are 30, 20, 10 and 15.
30 > 20 > 15 > 10
Reading story books has the highest remaining frequency, so it is the most popular activity among the four choices being compared.

Total for the two days = 30 + 40
= 70 saplings
The counts refer to separate days, so they are added. This gives the combined number planted on Wednesday and Thursday, rather than the difference between the two days.

Increase = Later count − Earlier count
= 3700 − 1400
= 2300
The figures are approximate, so the increase is about 2300 tigers. Adding the two counts would not measure the change between the years.

Difference in height = 8848 − 2228
= 6620 m
Both measurements are in metres, so they can be subtracted directly. A graph using a common scale should show this same difference between the two heights.

Only the heights are known. Making a triangle wider introduces an extra visual comparison that is not supported by those measurements. Equal-width bars compare heights more clearly because their widths do not suggest additional information about the mountains.

A column graph has bars that rise vertically. The heights of the columns show the quantities using a common scale. The bars can resemble upright pillars, which is why this form of bar graph is called a column graph.

In a frequency table, the tallies are used for counting occurrences.

Choosing an appropriate scale for data presentation is most important for clarity.