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Data Handling and Presentation

🎓 Class 6📖 Ganita Prakash📖 8 notes🧠 15 Q&A⏱️ ~12 min
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Data Handling and PresentationStudy Notes

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Introduction to Data Handling

Explanation

Introduction to Data Handling

Data handling is an essential part of mathematics that deals with collecting, organizing, and interpreting information. In our daily lives, we come across various types of data, such as the number of students in a class, the favorite games of children, or the number of books borrowed from a library. Handling data helps us to make sense of this information and draw meaningful conclusions. The process of data handling involves several steps: first, data collection through surveys or observations; second, organizing the data systematically; third, representing the data visually; and finally, interpreting the data to answer questions or solve problems. This chapter introduces these steps and explains how to work with data effectively. Understanding data handling helps students develop skills to analyze information critically and make informed decisions in real life. **Table on page 5 (1×7)** | Letter | c | e | i | r | x | Any other letter of your choice | | --- | --- | --- | --- | --- | --- | --- | | Number of times found in the news item | | | | | | | **Table on page 7 (3×2)** | Response | Number of Children ( = 10 Children) | | --- | --- | | Always | | | Sometimes | | | Never | | **Table on page 11 (7×4)** | | Day | Number of Books Borrowed | ( =1 Book ) | | --- | --- | --- | --- | | | Monday | | | | | Tuesday | | | | | Wednesday | | | | Thursday Friday Saturday a. On which day were the minimum number of books borrowed? b. What was the total number of books borrowed during the week? c. On which day were the maximum number of books borrowed? What may be the possible reason? 2. M agan 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 — Shopkeeper Number of Kites Sold Chaman 250 Rani 300 Rukhsana 100 Jasmeet 450 Jetha Lal 250 Poonam Ben 700 | | | | | | Thursday | | | | | Friday | | | | | Saturday | | | **Table on page 17 (1×9)** | Match | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Runs | 80 | 50 | 10 | 100 | 90 | 0 | 90 | 50 | **Table on page 20 (2×5)** | | | | | | | --- | --- | --- | --- | --- | | Mites | Caterpillars | Beetles | Butterflies | Grasshoppers | | 6 | 10 | 5 | 3 | 2 | **Table on page 20 (1×6)** | City | Vidisha | Jabalpur | Seoni | Indore | Sagar | | --- | --- | --- | --- | --- | --- | | Number of tickets | 24 | 20 | 16 | 28 | 16 | **Table on page 21 (10×7)** | Vidisha Jabalpur Seoni Indore Sagar City a. Write the number of tickets sold for Vidisha above the bar. b. Write the number of tickets sold for Jabalpur above the bar. 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? d. Draw the correct bar for Sagar. e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. f. Are the bars for Seoni and Indore correct in this graph? I not, draw the correct bar(s). 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.: bike car bike bus bike bike bike auto rickshaw bicycle bullock bicycle auto cart rickshaw car scooter car auto bicycle bike rickshaw car auto rickshaw bike scooter bike car bicycle scooter bicycle scooter bike bus auto rickshaw auto rickshaw bike bicycle bus bike bicycle scooter bus scooter auto bike rickshaw | | | | | | | | --- | --- | --- | --- | --- | --- | --- | | | bike | car | bike | bus | bike | bike | | | bike | auto rickshaw | bicycle | bullock cart | bicycle | auto rickshaw | | | car | scooter | car | auto rickshaw | bicycle | bike | | | car | auto rickshaw | bike | scooter | bike | car | | | bicycle | scooter | bicycle | scooter | bike | bus | | | auto rickshaw | auto rickshaw | bike | bicycle | bus | bike | | | bicycle | scooter | bus | scooter | auto rickshaw | bike | | | | | | | | | | | scooter | bicycle | bike | bullock cart | auto rickshaw | scooter | | | car | scooter | | | | |

  • Data handling involves collecting, organizing, and interpreting information.
  • Data can be collected through surveys, observations, or experiments.
  • Organizing data systematically makes it easier to understand and analyze.
  • Visual representation of data helps in better interpretation.
  • Data handling is used in everyday life for decision making.
  • The chapter covers various methods of data representation like tables, tally marks, pictographs, and bar graphs.
  • 📌 Data: Information collected for analysis.
  • 📌 Data handling: The process of collecting, organizing, and interpreting data.

Organising Data in Tables

Explanation

Organising Data in Tables

Once data is collected, it is important to organize it in a systematic way to make it easier to read and analyze. Tables are an effective method for organizing data. A table consists of rows and columns where data is arranged clearly. Each row typically represents a category or an item, and each column represents a characteristic or a value related to that category. Organizing data in tables helps in comparing different items and identifying patterns or trends. For example, a table listing students' names along with their favorite games helps us quickly see which games are popular. Tables can also include tally marks to show frequencies, making counting and summarizing easier. Properly constructed tables are the first step towards representing data visually through pictographs or bar graphs. **Table on page 2 (10×3)** | Mehnoor – Kabaddi | Pushkal – Satoliya (Pittu) | Anaya – Kabaddi | | --- | --- | --- | | Jubimon – Hockey | Densy – Badminton | Jivisha – Satoliya (Pittu) | | Simran – Kabaddi | Jivika – Satoliya (Pittu) | Rajesh – Football | | Nand – Satoliya (Pittu) | Leela – Hockey | Thara – Football | | Ankita – Kabaddi | Afshan – Hockey | Soumya – Cricket | | Imon – Hockey | Keerat – Cricket | Navjot – Hockey | | Yuvraj – Cricket | Gurpreet – Hockey | Hemal – Satoliya (Pittu) | | Rehana – Hockey | Arsh – Kabaddi | Debabrata – Football | | Aarna – Badminton | Bhavya – Cricket | Ananya – Hockey | | Kompal – Football | Sarah – Kabaddi | Hardik – Cricket | | Tahira – Cricket | | | **Table on page 3 (5×3)** | Sweets | Tally Marks | No. of Students | | --- | --- | --- | | Jalebi | |||| | | 6 | | Gulab jamun | |||| |||| | 9 | | Gujiya | |||| |||| ||| | ____________ | | Barfi | ||| | ____________ | | Rasgulla | |||| || | ____________ | **Table on page 6 (5×3)** | Modes of Travelling | Number of Students | = 1 Student | | --- | --- | --- | | Private car | | | | Public bus | | | | School bus | | | | Cycle | | | | Walking | | |

  • Tables organize data into rows and columns for clarity.
  • Each row represents an item or category; each column represents data attributes.
  • Tables help in comparing and analyzing data easily.
  • Tally marks can be used within tables to record frequencies.
  • Organized data in tables is useful for further representation like graphs.
  • Tables reduce confusion and make data interpretation straightforward.
  • 📌 Table: A systematic arrangement of data in rows and columns.
  • 📌 Row: Horizontal arrangement in a table representing an item or category.
  • 📌 Column: Vertical arrangement in a table representing data attributes.

Recording Data Using Tally Marks

Explanation

Recording Data Using Tally Marks

Tally marks are a simple and efficient way to record and count data as it is collected. Each tally mark represents one count. When counting, every group of five is represented by four vertical lines with a diagonal line crossing them, making it easy

Practice QuestionsData Handling and Presentation

Includes NCERT exercise questions with answers

Q1.For any two whole numbers x and y, which of the following suggests that operation of multiplication is commutative ?
A.x + y = y + x
B.x × y > y × x
C.x × y
D.x × y = y × x

Answer:

x × y = y × x

Explanation:

[{"id": "caf9285b-e655-4259-b525-a64fad22d56a", "type": "html", "value": " The commutative property of multiplication is given by x × y = y × x "}]

MediumNCERT
Q2.5 less than 8 times a number can be represented as _________
A.5x - 8
B.8x - 5
C.5 - 8x
D.8x + 5

Answer:

8x - 5

Explanation:

[{"id": "3707571d-9ed9-4d6c-a163-bd726257ebeb", "type": "html", "value": " Let the number be x. 8 times the number x can be represented as 8x 5 less than 8 times the number can be represented as 8x - 5 Correct expression is option 2 "}]

MediumNCERT
Q3.Which of the following is an equation?
A.m/4 = 1
B.m/4
C.m/4 > 1
D.m/4 + 1

Answer:

m/4 = 1

Explanation:

[{"id": "52324d7f-cc13-4f6b-9009-24b3e5cae842", "type": "html", "value": " Here m/4 = 1 is an equation because it has LHS i.e. m/4, RHS i.e. 0 and an equal sign in between LHS and RHS "}]

MediumNCERT
Q4.Height of a tree is 1 metre. After one year, its height is increased by h metre. What is the height of the tree after one year (in metres)?
A.1 × h
B.1 - h
C.1 + h
D.1 ÷ h

Answer:

1 + h

Explanation:

[{"id": "768a715b-0164-4d0e-905e-579726bc4d68", "type": "html", "value": " Height of a tree is 1 m After one year its height increased by h meters. So the height of tree becomes (1 + h) metres Correct answer is option 3 "}]

MediumNCERT
Q5.Roshani had ₹ x with her. She went to the market and purchased 20 pencils for ₹ 40, 2 erasers for ₹ 10 and 1 sharpener for ₹ 5. In addition to this, she also got ₹ 10 from her father. How much money is now left with Roshani?
A.₹ (x + 10)
B.₹ (x - 55)
C.₹ (x - 45)
D.₹ (x - 65)

Answer:

₹ (x - 45)

Explanation:

[{"id": "1146078c-972a-4a7b-96b0-39aa16892c7b", "type": "html", "value": " Roshani has ₹ x She purchased 20 pencils, 2 erasers and 1 sharpner of ₹ 40, ₹ 10 and ₹ 5, respectively. Therefore total money spent = 40 + 10 + 5 = ₹ 55 Money left with Roshani = ₹ (x - 55) Her father gave her ₹10 Money now left with Roshani = ₹ (x - 55 + 10) = ₹ (x - 45) The correct answer is option 3 "}]

MediumNCERT
Q6.There are 5 jars in sweets shop. x number of chocolates are added in each jar. If 10 chocolates are already present in one of the jars, then what is the total number of chocolates in the 5 jars?
A.10x + 5
B.5x + 10
C.5x
D.5x/10

Answer:

5x + 10

Explanation:

[{"id": "b7fbc24d-8f5f-4625-a5b9-3000f6451420", "type": "html", "value": " Number of jars = 5 Number of chocolates added in each jar = x Therefore, number of chocolates added in 5 jars = 5x It is given that 10 chocolates are already present in one of the jar. Therefore, total number of chocolates present in 5 jars = 5x + 10 So, option 2 is correct. "}]

MediumNCERT
Q7.Which of the following value of k satisfies the algebraic equation 8k - 38 = 2?
A.k = 1
B.k = 3
C.k = 5
D.k = 7

Answer:

k = 5

Explanation:

[{"id": "c043902c-4f44-407d-9724-b28716ab4d11", "type": "html", "value": " Given equation is 8k - 38 = 2 therefore, 8k = 38 + 2 8k = 40 k = 40/ 8 k = 5. Let's verify this. put the value k = 5 in 8k - 38 = 2 8(5) - 38 = 2 40 - 38 = 2 2 = 2 LHS = RHS Therefore, k = 5 is the correct solution. So, option 3 is correct. "}]

MediumNCERT
Q8.In which of the following case an angle can be called a copy of other angle?
A.If the two angles have the same vertex.
B.If the two angles have a common arm.
C.If the measure of both angles is the same.
D.If the length of arms of the two angles is same.

Answer:

If the measure of both angles is the same.

Explanation:

[{"id": "5b732179-57fa-439d-8c20-d8b877e3766e", "type": "html", "value": " One angle can be called copy of the other, only if the measure of both angles is the same. "}]

MediumNCERT