Class 6 : Maths ( English ) – Lesson 4. Data Handling and Presentation

EXPLANATION AND ANALYSIS

🌿 1. Introduction: Why Do We Need Data?

In our daily life, we constantly deal with information. We ask questions like:
How many students are present today?
Which fruit is liked by most students?
How many hours do we study in a week?

All such information, when collected in an organised way, is called data. Mathematics helps us not only to collect data but also to arrange, understand, and present it clearly so that meaningful conclusions can be drawn.

🔵 Data helps us make decisions
🟢 Data shows patterns and trends
🟡 Data makes comparisons easy
🔴 This chapter teaches how raw information becomes meaningful through organisation

🧠 2. What Is Data?

Data is a collection of facts, figures, or observations collected for a purpose.

🔹 Data may be numbers, words, or simple observations
🔹 Data is usually collected by counting, measuring, or asking questions
🔹 Data by itself may be confusing if not organised

💡 Concept:
Data = collected information

✏️ Note:
Unorganised data is called raw data.

🌱 3. Collection of Data

Data can be collected in many simple ways.

🔵 By counting objects
🟢 By asking questions (survey)
🟡 By observing situations
🔴 By measuring quantities

🔹 Example:
Counting the number of students who like different sports

💡 Concept:
Purpose decides what kind of data should be collected.

🧠 4. Raw Data

When data is first collected, it is usually unorganised.

🔹 Such data is called raw data
🔹 Raw data may contain repeated values
🔹 It is difficult to understand patterns directly from raw data

✏️ Note:
Raw data must be organised before interpretation.

🌿 5. Organising Data

To make sense of data, we arrange it systematically.

🔵 Data can be arranged in ascending or descending order
🟢 Repeated values can be grouped together
🟡 This arrangement helps in easy counting and comparison

🔹 Example:
Marks obtained by students arranged from lowest to highest

💡 Concept:
Organisation makes data meaningful.

🧠 6. Tally Marks

Tally marks are a simple way of counting frequencies.

🔹 Each occurrence is marked using a vertical line
🔹 The fifth mark is shown by crossing four lines
🔹 Tally marks make counting quick and accurate

✏️ Note:
Tally marks are always written in groups of five.

🌱 7. Frequency

The number of times a particular value occurs in data is called its frequency.

🔵 Frequency tells how common a value is
🟢 Higher frequency means greater occurrence
🟡 Frequency helps in comparison

💡 Concept:
Frequency = number of occurrences

🧠 8. Frequency Table

A frequency table shows values along with their frequencies.

🔹 It usually has two columns: data values and frequency
🔹 It summarises large data into a compact form
🔹 It is the base for drawing graphs later

✏️ Note:
Frequency tables must be neat and accurate.

🌿 9. Pictograph

A pictograph represents data using pictures or symbols.

🔵 Each picture represents a fixed number
🟢 It makes data attractive and easy to understand
🟡 Suitable for small sets of data

🔹 Example:
One 🟦 may represent 5 students

💡 Concept:
Always check the value of one symbol in a pictograph.

🧠 10. Bar Graph

A bar graph represents data using rectangular bars.

🔵 Bars can be vertical or horizontal
🟢 Height or length of bar shows frequency
🟡 All bars have equal width

🔹 Bar graphs help in clear comparison between categories

✏️ Note:
Scale must be chosen carefully while drawing bar graphs.

🌍 11. Interpreting Graphs

Once data is presented using graphs, we can answer questions.

🔹 Which value is the highest?
🔹 Which value is the lowest?
🔹 What is the difference between two categories?

🧠 Interpretation means understanding what the graph is telling us.

💡 Concept:
Graphs help us see information quickly.

🧠 12. Importance of Data Handling

Data handling is used everywhere.

🔵 Weather reports
🟢 School records
🟡 Sports statistics
🔴 Government surveys

🔹 It helps in decision-making and planning
🔹 It develops logical and analytical thinking

💡 Concept:
Data handling connects mathematics with real life.

📘 Summary

The chapter Data Handling and Presentation introduces students to the systematic way of dealing with information. Data is collected through counting, observing, or surveying and is initially unorganised as raw data. To make sense of this data, it must be organised using ordering, tally marks, and frequency tables. These methods help us understand how often each value occurs.

Data can be presented visually using pictographs and bar graphs, which make comparison simple and clear. Graphical representation helps us interpret information quickly and accurately. This chapter shows how mathematics helps us organise real-life information and draw meaningful conclusions from it.

📝 Quick Recap

🟢 Data is collected information
🟡 Raw data is unorganised data
🔵 Tally marks help in counting
🔴 Frequency shows number of occurrences
⚡ Pictographs and bar graphs present data visually
🧠 Data handling helps in decision-making

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TEXTBOOK QUESTIONS

📝 Figure it out

🌿 1. Pictographs

🌿 2. Bar Graphs

🔒 ❓ Question 1
The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori.

📌 ✅ Answer (Understanding the pictograph first)
🔹 Each picture of a book represents 1 book.
🔹 We count the number of book symbols shown for each day.

🔹 Monday
🔸 Number of book symbols = 6
✔️ Books borrowed on Monday = 6

🔹 Tuesday
🔸 Number of book symbols = 4
✔️ Books borrowed on Tuesday = 4

🔹 Wednesday
🔸 Number of book symbols = 3
✔️ Books borrowed on Wednesday = 3

🔹 Thursday
🔸 Number of book symbols = 0
✔️ Books borrowed on Thursday = 0

🔹 Friday
🔸 Number of book symbols = 5
✔️ Books borrowed on Friday = 5

🔹 Saturday
🔸 Number of book symbols = 7
✔️ Books borrowed on Saturday = 7

🔒 ❓ Question 1(a)
On which day were the minimum number of books borrowed?

📌 ✅ Answer
🔹 Thursday shows no book symbols.
✔️ Final: Thursday had the minimum number of books borrowed.

🔒 ❓ Question 1(b)
What was the total number of books borrowed during the week?

📌 ✅ Answer (Step-by-step addition)
🔵 Step 1: Monday = 6
🔵 Step 2: Tuesday = 4
🔵 Step 3: Wednesday = 3
🔵 Step 4: Thursday = 0
🔵 Step 5: Friday = 5
🔵 Step 6: Saturday = 7

🔵 Step 7: Total = 6 + 4 + 3 + 0 + 5 + 7
🔵 Step 8: Total = 25

✔️ Final: 25 books were borrowed during the week.

🔒 ❓ Question 1(c)
On which day were the maximum number of books borrowed? What may be the possible reason?

📌 ✅ Answer
🔹 Saturday shows the highest number of book symbols (7).
✔️ Final: Saturday had the maximum number of books borrowed.

🔹 Possible reason (student-friendly explanation):
🔸 Students may have more free time before holidays.
🔸 They may borrow books to read during Sunday or vacations.

✔️ Final: Maximum books were borrowed on Saturday, possibly due to more free time.

🔒 ❓ Question 2
Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold to these six shopkeepers are given below.

Chaman – 250
Rani – 300
Rukhsana – 100
Jasmeet – 450
Jetha Lal – 250
Poonam Ben – 700

Prepare a pictograph using the symbol ♦ to represent 100 kites. Answer the following questions.

📌 ✅ Answer (Understanding the pictograph first)
🔹 One symbol ♦ represents 100 kites.
🔹 To find the number of symbols, divide the number of kites by 100.

🔹 Chaman
🔸 250 ÷ 100 = 2.5 symbols

🔹 Rani
🔸 300 ÷ 100 = 3 symbols

🔹 Rukhsana
🔸 100 ÷ 100 = 1 symbol

🔹 Jasmeet
🔸 450 ÷ 100 = 4.5 symbols

🔹 Jetha Lal
🔸 250 ÷ 100 = 2.5 symbols

🔹 Poonam Ben
🔸 700 ÷ 100 = 7 symbols

🔒 ❓ Question 2(a)
How many symbols represent the kites that Rani purchased?

📌 ✅ Answer
🔹 Rani purchased 300 kites.
🔹 Each symbol represents 100 kites.
🔹 300 ÷ 100 = 3.
✔️ Final: 3 symbols represent the kites Rani purchased.

🔒 ❓ Question 2(b)
Who purchased the maximum number of kites?

📌 ✅ Answer
🔹 Comparing all the values, 700 kites is the highest number.
🔹 Poonam Ben purchased 700 kites.
✔️ Final: Poonam Ben purchased the maximum number of kites.

🔒 ❓ Question 2(c)
Who purchased more kites, Jasmeet or Chaman?

📌 ✅ Answer
🔹 Jasmeet purchased 450 kites.
🔹 Chaman purchased 250 kites.
🔹 450 is greater than 250.
✔️ Final: Jasmeet purchased more kites than Chaman.

🔒 ❓ Question 2(d)
Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?

📌 ✅ Answer (Teacher-style explanation)
🔹 Rani purchased 300 kites.
🔹 Double of 300 = 600 kites.
🔹 Poonam Ben purchased 700 kites.
🔹 700 is greater than 600.
✔️ Final: Yes, Rukhsana is correct, because Poonam Ben purchased more than double the number of kites that Rani purchased.

🌿 3. Drawing a Bar Graphs

🔒 ❓ Question 1
Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected:

Mites – 6
Caterpillars – 10
Beetles – 5
Butterflies – 3
Grasshoppers – 2

Help her prepare a bar graph representing this data.

📌 ✅ Answer (Teacher-style explanation)
🔹 First, draw two axes.
🔹 On the horizontal axis, write the names of insects: Mites, Caterpillars, Beetles, Butterflies, Grasshoppers.
🔹 On the vertical axis, write numbers starting from 0 up to at least 10.
🔹 Choose a suitable scale, for example: 1 unit = 1 insect.
🔹 Draw bars of the following heights:
🔸 Mites = 6 units
🔸 Caterpillars = 10 units
🔸 Beetles = 5 units
🔸 Butterflies = 3 units
🔸 Grasshoppers = 2 units
✔️ Final: A correct bar graph shows Caterpillars as the tallest bar and Grasshoppers as the shortest bar.

🔒 ❓ Question 2
Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a two-hour period.

Vidisha – 24
Jabalpur – 20
Seoni – 16
Indore – 28
Sagar – 16

She used this data and prepared a bar graph on the board, but someone erased a portion of the graph.

🔒 ❓ Question 2(a)
Write the number of tickets sold for Vidisha above the bar.

📌 ✅ Answer
🔹 From the given data, Vidisha has 24 tickets.
✔️ Final: 24

🔒 ❓ Question 2(b)
Write the number of tickets sold for Jabalpur above the bar.

📌 ✅ Answer
🔹 From the given data, Jabalpur has 20 tickets.
✔️ Final: 20

🔒 ❓ Question 2(c)
The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?

📌 ✅ Answer (Step-by-step reasoning)
🔹 Vidisha: 24 tickets shown by 6 units
🔹 24 ÷ 6 = 4
🔹 Jabalpur: 20 tickets shown by 5 units
🔹 20 ÷ 5 = 4
✔️ Final: Scale is 1 unit length = 4 tickets

🔒 ❓ Question 2(d)
Draw the correct bar for Sagar.

📌 ✅ Answer
🔹 Sagar has 16 tickets.
🔹 Using the scale 1 unit = 4 tickets,
🔹 16 ÷ 4 = 4 units.
✔️ Final: The bar for Sagar should be 4 unit lengths high.

🔒 ❓ Question 2(e)
Add the scale of the bar graph by placing the correct numbers on the vertical axis.

📌 ✅ Answer
🔹 Scale: 1 unit = 4 tickets.
🔹 Vertical axis numbers should be:
0, 4, 8, 12, 16, 20, 24, 28
✔️ Final: These numbers correctly represent the scale on the vertical axis.

🔒 ❓ Question 2(f)
Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).

📌 ✅ Answer
🔹 Seoni has 16 tickets, so its bar should be 4 units high.
🔹 Indore has 28 tickets, so its bar should be 7 units high.
🔹 By comparing with the given graph, the bars do not match these unit heights.
✔️ Final: The bars for Seoni and Indore are not correct and must be redrawn with heights of 4 units and 7 units respectively.

🔒 ❓ Question 3
Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.

a. Prepare a frequency distribution table for the data.

📌 ✅ Answer (Correct NCERT approach)
🔹 Carefully observe the list of vehicles given in the table.
🔹 Count each type of transport one by one.
🔹 Use tally marks while counting to avoid mistakes.
🔹 After counting, write the final totals in a frequency table.

✏️ Note (Important for students):
This is a data-counting activity. The marks are for the method of counting and tabulation, not for memorising fixed numbers.

✔️ Final: A correct frequency distribution table is prepared by accurate counting using tally marks.

🔒 ❓ Question 3(b)
Which means of transport was used the most?

📌 ✅ Answer
🔹 Look at the completed frequency table.
🔹 Identify the transport with the highest frequency.
✔️ Final: The means of transport with the maximum count was used the most.

🔒 ❓ Question 3(c)
If you were there to collect this data, how could you do it? Write the steps or process.

📌 ✅ Answer (Teacher-style steps)
🔹 Stand at a place where the road is clearly visible.
🔹 Keep a notebook and pencil ready.
🔹 Each time a vehicle passes, put a tally mark for that vehicle.
🔹 Continue counting for the given time (9 a.m. to 10 a.m.).
🔹 After the time ends, count the tally marks for each type of transport.
✔️ Final: This step-by-step process ensures systematic and accurate data collection.

🔒 ❓ Question 4
Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared:

a. The minimum number of times.
b. The maximum number of times.
c. Numbers that appeared an equal number of times.

📌 ✅ Answer (NCERT-safe explanation)
🔹 This is an activity-based question.
🔹 Different students may get different results.
🔹 What matters is the correct method, not identical answers.

🔹 Correct method:
🔸 Roll the die 30 times.
🔸 Record each outcome using tally marks.
🔸 Prepare a frequency table for numbers 1 to 6.
🔸 Compare the frequencies.

🔒 ❓ Question 4(a)
Which number appeared the minimum number of times?

📌 ✅ Answer
🔹 Look at the frequency table you prepared.
🔹 Identify the number with the smallest frequency.
✔️ Final: The number with the least count appeared the minimum number of times.

🔒 ❓ Question 4(b)
Which number appeared the maximum number of times?

📌 ✅ Answer
🔹 Observe the frequency table.
🔹 Identify the number with the highest frequency.
✔️ Final: The number with the greatest count appeared the maximum number of times.

🔒 ❓ Question 4(c)
Find numbers that appeared an equal number of times.

📌 ✅ Answer
🔹 Compare the frequencies of all numbers from 1 to 6.
🔹 Identify numbers having the same frequency.
✔️ Final: Numbers with equal frequencies are the required answer.

🔒 ❓ Question 5
Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches.

Wickets Taken → Number of Matches
0 → 2
1 → 4
2 → 6
3 → 8
4 → 3
5 → 5
6 → 1
7 → 1

🔒 ❓ Question 5(a)
What information is this table giving?

📌 ✅ Answer (Teacher-style explanation)
🔹 The table shows how many wickets Jaspreet Bumrah took in different matches.
🔹 It also tells us how many matches correspond to each wicket count.
✔️ Final: The table gives information about the distribution of wickets taken by Bumrah across his last 30 matches.

🔒 ❓ Question 5(b)
What may be the title of this table?

📌 ✅ Answer
🔹 A good title should clearly explain what the data is about.
✔️ Final:
“Frequency Distribution of Wickets Taken by Jaspreet Bumrah in His Last 30 Matches”

🔒 ❓ Question 5(c)
What caught your attention in this table?

📌 ✅ Answer (Student-friendly explanation)
🔹 Bumrah took 3 wickets in the highest number of matches (8 matches).
🔹 He took 6 and 7 wickets only once each, which is very rare.
✔️ Final: The most noticeable point is that 3 wickets occurred most frequently, while very high wicket counts occurred rarely.

🔒 ❓ Question 5(d)
In how many matches has Bumrah taken 4 wickets?

📌 ✅ Answer
🔹 From the table, the number of matches corresponding to 4 wickets is 3.
✔️ Final: Bumrah took 4 wickets in 3 matches.

🔒 ❓ Question 5(e)
Mayank says, “If we want to know the total number of wickets he has taken in his last 30 matches, we have to add the numbers 0, 1, 2, 3, … up to 7.” Can Mayank get the total number of wickets taken in this way? Why?

📌 ✅ Answer (Conceptual explanation)
🔹 Adding only 0, 1, 2, 3, …, 7 ignores how many times each value occurs.
🔹 Some wicket numbers happened many times, others very few times.
🔹 So this method does not use the frequency data.
✔️ Final: No, Mayank cannot get the correct total this way because he is not considering the number of matches for each wicket count.

🔒 ❓ Question 5(f)
How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?

📌 ✅ Answer (Step-by-step method)
🔹 Multiply each wicket count by the number of matches in which it occurred.
🔹 Then add all these results.

🔹 Calculation explained clearly:
🔸 0 × 2 = 0
🔸 1 × 4 = 4
🔸 2 × 6 = 12
🔸 3 × 8 = 24
🔸 4 × 3 = 12
🔸 5 × 5 = 25
🔸 6 × 1 = 6
🔸 7 × 1 = 7

🔹 Now add them:
0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90

✔️ Final: The total number of wickets taken by Bumrah in his last 30 matches is 90.

🔒 ❓ Question 6
The following pictograph shows the number of tractors in five different villages.
( 🚜 = 1 tractor )

From the pictograph, we observe:

🔹 Village A → 7 tractors
🔹 Village B → 5 tractors
🔹 Village C → 9 tractors
🔹 Village D → 4 tractors
🔹 Village E → 8 tractors

🔒 ❓ Question 6(a)
Which village has the smallest number of tractors?

📌 ✅ Answer
🔹 Village D has 4 tractors, which is the least among all villages.
✔️ Final: Village D

🔒 ❓ Question 6(b)
Which village has the most tractors?

📌 ✅ Answer
🔹 Village C has 9 tractors, which is the highest number shown.
✔️ Final: Village C

🔒 ❓ Question 6(c)
How many more tractors does Village C have than Village B?

📌 ✅ Answer (Step-by-step)
🔹 Tractors in Village C = 9
🔹 Tractors in Village B = 5
🔹 Difference = 9 − 5 = 4
✔️ Final: Village C has 4 more tractors than Village B.

🔒 ❓ Question 6(d)
Komal says, “Village D has half the number of tractors as Village E.” Is she right?

📌 ✅ Answer (Conceptual explanation)
🔹 Tractors in Village D = 4
🔹 Tractors in Village E = 8
🔹 Half of 8 = 4
✔️ Final: Yes, Komal is right, because Village D has exactly half the number of tractors as Village E.

🔒 ❓ Question 7
The number of girl students in each class of a school is depicted by the pictograph.
( 👧 = 4 girls )

From the pictograph, we observe:

🔹 Class 1 → 6 full symbols = 6 × 4 = 24 girls
🔹 Class 2 → 4 full + 1 half = (4 × 4) + 2 = 18 girls
🔹 Class 3 → 5 full symbols = 5 × 4 = 20 girls
🔹 Class 4 → 3 full + 1 half = (3 × 4) + 2 = 14 girls
🔹 Class 5 → 2 full + 1 half = (2 × 4) + 2 = 10 girls
🔹 Class 6 → 4 full symbols = 4 × 4 = 16 girls
🔹 Class 7 → 3 full symbols = 3 × 4 = 12 girls
🔹 Class 8 → 1 full + 1 half = 4 + 2 = 6 girls

🔒 ❓ Question 7(a)
Which class has the least number of girl students?

📌 ✅ Answer
🔹 Class 8 has 6 girls, which is the smallest number.
✔️ Final: Class 8

🔒 ❓ Question 7(b)
What is the difference between the number of girls in Class 5 and Class 6?

📌 ✅ Answer (Step-by-step)
🔹 Girls in Class 5 = 10
🔹 Girls in Class 6 = 16
🔹 Difference = 16 − 10 = 6
✔️ Final: The difference is 6 girls.

🔒 ❓ Question 7(c)
If two more girls were admitted in Class 2, how would the graph change?

📌 ✅ Answer (Conceptual explanation)
🔹 Class 2 currently has 18 girls.
🔹 After admitting 2 more girls, total = 18 + 2 = 20 girls.
🔹 In the pictograph, 20 girls are shown by 5 full symbols.
✔️ Final: The half symbol in Class 2 would become a full symbol, making 5 complete symbols.

🔒 ❓ Question 7(d)
How many girls are there in Class 7?

📌 ✅ Answer
🔹 Class 7 shows 3 full symbols.
🔹 3 × 4 = 12.
✔️ Final: There are 12 girls in Class 7.

🔒 ❓ Question 8
Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka’s Bagalkote and Vijaypura districts. The number of Mudhol dogs in six villages of Karnataka are as follows:

Village A – 18
Village B – 36
Village C – 12
Village D – 48
Village E – 18
Village F – 24

Prepare a pictograph and answer the following questions.

🔒 ❓ Question 8(a)
What will be a useful scale or key to draw this pictograph?

📌 ✅ Answer (Teacher-style explanation)
🔹 All numbers are multiples of 6.
🔹 Choosing a scale that divides all values evenly makes the pictograph neat and simple.
✔️ Final: A useful scale is 1 symbol = 6 dogs.

🔒 ❓ Question 8(b)
How many symbols will you use to represent the dogs in Village B?

📌 ✅ Answer (Step-by-step)
🔹 Dogs in Village B = 36
🔹 Scale = 1 symbol represents 6 dogs
🔹 36 ÷ 6 = 6
✔️ Final: 6 symbols will be used for Village B.

🔒 ❓ Question 8(c)
Kamini said that the number of these dogs in Village B and Village D together will be more than the number of these dogs in the other 4 villages. Is she right? Give reasons for your response.

📌 ✅ Answer (Logical reasoning)
🔹 Dogs in Village B = 36
🔹 Dogs in Village D = 48
🔹 Total in B and D = 36 + 48 = 84

🔹 Dogs in other villages:
Village A = 18
Village C = 12
Village E = 18
Village F = 24

🔹 Total in A, C, E, F = 18 + 12 + 18 + 24 = 72

🔹 84 is greater than 72
✔️ Final: Yes, Kamini is right, because Villages B and D together have more dogs than the other four villages combined.

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🔒 ❓ Question 9
A survey of 120 school students was conducted to find out which activity they preferred to do in their free time:

Playing – 45
Reading story books – 30
Watching TV – 20
Listening to music – 10
Painting – 15

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?

📌 ✅ Answer (Bar graph explanation)
🔹 First draw the horizontal axis and write the activities.
🔹 Draw the vertical axis and mark numbers using the scale 1 unit = 5 students.
🔹 Heights of bars will be:
🔸 Playing → 45 ÷ 5 = 9 units
🔸 Reading story books → 30 ÷ 5 = 6 units
🔸 Watching TV → 20 ÷ 5 = 4 units
🔸 Listening to music → 10 ÷ 5 = 2 units
🔸 Painting → 15 ÷ 5 = 3 units

🔒 ❓ Which activity is preferred by most students other than playing?

📌 ✅ Answer
🔹 After playing, the highest number of students prefer reading story books (30 students).
✔️ Final: Reading story books is preferred by most students other than playing.

🔒 ❓ Question 10
Students and teachers of a primary school decided to plant tree saplings during the first week of July. The bar graph shows the number of saplings planted on different days.

From the bar graph, we read:

🔹 Monday → 50 saplings
🔹 Tuesday → 40 saplings
🔹 Wednesday → 30 saplings
🔹 Thursday → 40 saplings
🔹 Friday → 50 saplings
🔹 Saturday → 60 saplings
🔹 Sunday → 40 saplings

🔒 ❓ Question 10(a)
The total number of saplings planted on Wednesday and Thursday is ______.

📌 ✅ Answer
🔹 Saplings on Wednesday = 30
🔹 Saplings on Thursday = 40
🔹 Total = 30 + 40 = 70
✔️ Final: 70 saplings

🔒 ❓ Question 10(b)
The total number of saplings planted during the whole week is ______.

📌 ✅ Answer (Step-by-step addition)
🔹 50 + 40 + 30 + 40 + 50 + 60 + 40
🔹 = 310
✔️ Final: 310 saplings

🔒 ❓ Question 10(c)
The greatest number of saplings were planted on ______ and the least number of saplings were planted on ______.
Why do you think that is the case? Why were more saplings planted on certain days and less on others? How could you try and figure out whether your explanations are correct?

📌 ✅ Answer (Reasoning + real-life thinking)
🔹 The greatest number of saplings were planted on Saturday (60).
🔹 The least number of saplings were planted on Wednesday (30).

🔹 Possible reasons:
🔸 More people may be free on weekends like Saturday.
🔸 Fewer saplings may be planted on working or school days.
🔸 Weather or availability of helpers can affect the count.

🔹 To check if these reasons are correct:
🔸 Talk to the organisers or teachers.
🔸 Check attendance records.
🔸 Observe future plantation drives.

✔️ Final: Saturday had the maximum and Wednesday had the minimum due to differences in participation and availability.

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🔒 ❓ Question 11
The number of tigers in India was recorded between 2006 and 2022. A frequency table and a bar graph were prepared, but there are a few mistakes in the graph. Identify and correct them.

Given data (from the table):

🔹 2006 → 1400 tigers
🔹 2010 → 1700 tigers
🔹 2014 → 2200 tigers
🔹 2018 → 3000 tigers
🔹 2022 → 3700 tigers

📌 ✅ Answer (Careful observation & correction)
🔹 The bar graph does not match the values in the table.
🔹 Some bars are either too short or too long compared to the actual numbers.
🔹 The scale on the horizontal axis is not used correctly for all years.
🔹 The bars should increase steadily from 2006 to 2022.

✔️ Correct representation should show:
🔸 Shortest bar for 2006 (1400)
🔸 Gradual increase in 2010 and 2014
🔸 Much taller bars for 2018 (3000) and 2022 (3700)

✔️ Final: The mistakes are in bar lengths and scale usage, and correcting them requires drawing each bar exactly according to the table values.

🌿 4. Artistic and Aesthetic Considerations

🔒 ❓ Question 1
If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?

📌 ✅ Answer
🔹 Heights are numerical values that are easy to compare when shown vertically.
🔹 The names of classes can be written on the horizontal axis.
🔹 The height values can be shown clearly on the vertical axis.
✔️ Final: A bar graph with vertical bars should be used because it clearly compares heights across different classes.

🔒 ❓ Question 2
If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar graph with vertical bars or with horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph. Which continents have the longest rivers?

📌 ✅ Answer (Explanation + example)
🔹 The names of continents and rivers are long.
🔹 Writing long names is easier and clearer in a horizontal bar graph.
✔️ Final: A horizontal bar graph is more suitable.

🔹 Example information (approximate values):
🔸 Africa → Nile → about 6650 km
🔸 South America → Amazon → about 6400–7000 km
🔸 Asia → Yangtze → about 6300 km
🔸 North America → Mississippi–Missouri → about 6275 km
🔸 Europe → Volga → about 3530 km
🔸 Australia → Murray–Darling system → about 3600–3700 km

🔹 Representation method:
🔸 Make a table with columns: Continent and Length of longest river.
🔸 Draw a horizontal bar graph with river length on the horizontal axis.

🔒 ❓ Which continents have the longest rivers?

📌 ✅ Answer
🔹 Africa has the longest river (Nile).
🔹 South America and Asia also have very long rivers.
✔️ Final: Africa, followed by South America and Asia, have the longest rivers.

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OTHER IMPORTANT QUESTIONS

(CBSE MODEL QUESTION PAPER)

ESPECIALLY MADE FROM THIS CHAPTER ONLY

🔵 Section A — Very Short Answer (1 mark each)

🔒 ❓ Question 1
What is data?
📌 ✅ Answer:
🔹 Data is a collection of facts, figures, or information

🔒 ❓ Question 2
What is raw data?
📌 ✅ Answer:
🔹 Raw data is data that is unorganised and collected for the first time

🔒 ❓ Question 3
Name one way of collecting data.
📌 ✅ Answer:
🔹 Data can be collected by counting objects

🔒 ❓ Question 4
What do tally marks represent?
📌 ✅ Answer:
🔹 Tally marks are used to count the number of occurrences

🔒 ❓ Question 5
How many tally marks make one group?
📌 ✅ Answer:
🔹 One group has five tally marks

🔒 ❓ Question 6
True or False:
Frequency tells how many times a value occurs.
📌 ✅ Answer:
🔹 Frequency shows number of occurrences
✔️ Final: True

🟢 Section B — Short Answer I (2 marks each)

🔒 ❓ Question 7
What is meant by frequency?
📌 ✅ Answer:
🔹 Frequency is the number of times a particular value occurs in data
🔸 It shows how common a value is

🔒 ❓ Question 8
Write any two methods of presenting data.
📌 ✅ Answer:
🔹 Pictograph
🔸 Bar graph

🔒 ❓ Question 9
What is a pictograph?
📌 ✅ Answer:
🔹 A pictograph represents data using pictures or symbols
🔸 Each picture stands for a fixed number

🔒 ❓ Question 10
What is a bar graph?
📌 ✅ Answer:
🔹 A bar graph represents data using rectangular bars
🔸 Length or height of bars shows frequency

🔒 ❓ Question 11
Why is data organised before presentation?
📌 ✅ Answer:
🔹 Organised data is easy to understand
🔸 It helps in comparison and interpretation

🔒 ❓ Question 12
Write one use of data handling in daily life.
📌 ✅ Answer:
🔹 Data handling is used in weather reports

🟡 Section C — Short Answer II (3 marks each)

🔒 ❓ Question 13
Explain the difference between data and raw data.

📌 ✅ Answer:
🔹 Data is collected information used for a specific purpose
🔹 Raw data is the data collected in its original, unorganised form
🔸 Raw data needs to be arranged before interpretation

🔒 ❓ Question 14
Name any three ways of collecting data.

📌 ✅ Answer:
🔹 By counting objects
🔹 By asking questions through a survey
🔸 By observing events or situations

🔒 ❓ Question 15
Why are tally marks used while organising data?

📌 ✅ Answer:
🔹 Tally marks help in counting data easily
🔹 They reduce chances of counting mistakes
🔸 Grouping in fives makes calculation quick

🔒 ❓ Question 16
What is a frequency table? State its use.

📌 ✅ Answer:
🔹 A frequency table shows data values along with their frequencies
🔹 It organises large data in a compact form
🔸 It helps in drawing graphs and comparisons

🔒 ❓ Question 17
What information can we get from a pictograph?

📌 ✅ Answer:
🔹 A pictograph shows data using pictures or symbols
🔹 It helps us compare quantities visually
🔸 It shows which category has more or less data

🔒 ❓ Question 18
Why should the scale be chosen carefully while drawing a bar graph?

📌 ✅ Answer:
🔹 Scale decides the value represented by each unit
🔹 Wrong scale can give incorrect interpretation
🔸 Proper scale makes the graph clear and accurate

🔒 ❓ Question 19
How does organising data help in interpretation?

📌 ✅ Answer:
🔹 Organised data is easy to read
🔹 It helps identify highest and lowest values
🔸 It allows quick comparison between categories

🔒 ❓ Question 20
Give two differences between a pictograph and a bar graph.

📌 ✅ Answer:
🔹 Pictograph uses pictures or symbols, bar graph uses bars
🔹 Pictograph is suitable for small data, bar graph for larger data sets

🔒 ❓ Question 21
What is meant by interpretation of data?

📌 ✅ Answer:
🔹 Interpretation means understanding the information shown by data
🔹 It helps answer questions based on graphs or tables
🔸 It leads to conclusions and decisions

🔒 ❓ Question 22
State two situations where data handling is useful.

📌 ✅ Answer:
🔹 In school records like attendance and marks
🔸 In sports to compare scores and performances

🔴 Section D — Long Answer (4 marks each)

🔒 ❓ Question 23
Explain why data needs to be organised before presentation.

📌 ✅ Answer:
🔹 Raw data is unorganised and difficult to understand directly
🔹 Organising data groups similar values together
🔹 It reduces confusion and counting errors
🔸 Organised data helps in easy comparison and interpretation

🔒 ❓ Question 24
Describe the steps involved in preparing a frequency table from raw data.

📌 ✅ Answer:
🔹 Step 1: List all data values from raw data
🔹 Step 2: Use tally marks to count each occurrence
🔹 Step 3: Count the tally marks carefully
🔸 Step 4: Write the total occurrences as frequency

🔒 ❓ Question 25
What is a pictograph? Write two advantages and one limitation of a pictograph.

📌 ✅ Answer:
🔹 A pictograph represents data using pictures or symbols
🔹 Advantage 1: It is easy to understand
🔹 Advantage 2: It is visually attractive
🔸 Limitation: It is not suitable for very large data sets

🔒 ❓ Question 26
Explain a bar graph and state the important points to be kept in mind while drawing it.

📌 ✅ Answer:
🔹 A bar graph uses rectangular bars to represent data
🔹 The height or length of each bar shows frequency
🔹 All bars should have equal width
🔹 Proper scale should be chosen
🔸 Bars should be drawn with equal spacing

🔒 ❓ Question 27
OR
Explain the importance of choosing a correct scale while drawing a bar graph.

📌 ✅ Answer:
🔹 Scale shows how much value one unit represents
🔹 Incorrect scale can misrepresent data
🔹 Proper scale makes comparison accurate
🔸 It helps in correct interpretation of information

🔒 ❓ Question 28
How does interpretation of data help in decision-making? Explain with examples.

📌 ✅ Answer:
🔹 Interpretation helps understand trends and patterns
🔹 It shows highest and lowest values clearly
🔹 Example: Choosing the most popular sport based on student preference data
🔸 Decisions become logical and evidence-based

🔒 ❓ Question 29
Explain with examples how data handling is useful in daily life.

📌 ✅ Answer:
🔹 Schools use data to maintain attendance and exam records
🔹 Weather departments use data to forecast weather
🔹 Shops use sales data to plan stock
🔸 Governments use data for surveys and planning

🔒 ❓ Question 30
OR
A student collects data about the number of books read by classmates in a month.
Explain how this data can be organised and presented.

📌 ✅ Answer:
🔹 First, list all collected numbers as raw data
🔹 Arrange data in ascending order
🔹 Use tally marks to count frequencies
🔹 Prepare a frequency table
🔸 Present data using a pictograph or bar graph

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