Chapter 4 • Ganita Prakash

Data Handling and Presentation

Learn how to collect, organize, and represent data using lists, tally mark tables, frequency distributions, ascending order arrays, and pictographs.

What is Data?

If you ask your classmates about their favourite colours, you will get a list of colours. This list is an example of data. Similarly, if you measure the weight of each student in your class, you would get a collection of measures of weight—again data.

Definition: Any collection of facts, numbers, measures, observations, or other descriptions of things that convey information about those things is called data.

We live in an age of information. We constantly see large amounts of data presented to us in new and interesting ways. In this chapter, we explore how data is presented, and how to correctly display, interpret, and make inferences from it!

4.1 Collecting and Organising Data

Navya and Naresh discussed finding the most popular game in their class. Naresh and Navya decided to ask each student in the class and prepare a raw list of responses:

Raw Collected Data (Favourite Games)

  • Mehnoor - Kabaddi | Pushkal - Satoliya (Pittu) | Anaya - Kabaddi
  • Jubimon - Hockey | Densy - Badminton | Jivisha - Satoliya (Pittu)
  • Simran - Kabaddi | Nand - Satoliya (Pittu) | Jivika - Satoliya (Pittu)
  • Leela - Hockey | Rajesh - Football | Thara - Football
  • Ankita - Kabaddi | Afshan - Hockey | Soumya - Cricket
  • Imon - Hockey | Keerat - Cricket | Navjot - Hockey
  • Yuvraj - Cricket | Rehana - Hockey | Gurpreet - Hockey
  • Arsh - Kabaddi | Hemal - Satoliya (Pittu) | Debabrata - Football
  • Aarna - Badminton | Kompal - Football | Bhavya - Cricket
  • Sarah - Kabaddi | Ananya - Hockey | Hardik - Cricket | Tahira - Cricket

4.1.1 Tally Marks & Frequency

To organize raw data effectively, we can use tally marks. A tally mark '|' represents 1 student. When the count reaches 5, we put a diagonal line through the previous four ($|||| \!\!\!\! \backslash$).

Example Table: New Year Sweets Preference (Shri Nilesh's Class)
Sweets Tally Marks No. of Students (Frequency)
Jalebi $|||| \!\!\!\! \backslash \ \ |$ 6
Gulab jamun $|||| \!\!\!\! \backslash \ \ ||||$ 9
Gujiya $|||| \!\!\!\! \backslash \ \ ||$ 7
Barfi $|||$ 3
Rasgulla $|||| \!\!\!\! \backslash$ 5

Frequency: The numbers 6, 9, 7, 3, 5 are the frequencies of preferences for jalebi, gulab jamun, gujiya, barfi, and rasgulla respectively.

4.1.2 Ascending Order & Arrays

Sushri Sandhya recorded shoe sizes of students in her class:

Raw Data: 4, 5, 3, 4, 3, 4, 5, 5, 4, 5, 5, 4, 5, 6, 4, 3, 5, 6, 4, 6, 4, 5, 7, 5, 6, 4, 5

Arranged in Ascending Order:

3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7

  • Smallest Shoe Size: 3
  • Largest Shoe Size: 7
  • Students with Size 5: 10 students
  • Students with Size > 4: 15 students (10 wearing size 5 + 4 wearing size 6 + 1 wearing size 7)

4.1.3 Data Activities & Letter Frequency

In a newspaper letter analysis activity, counting occurrences of specific letters usually yields a predictable order due to English language properties:

Letter Frequency Pattern

Expected ascending order of frequency: x, c, r, i, e

Vowels like 'e' and 'i' appear far more frequently than rare consonants like 'x'.

4.2 Pictographs

A pictograph represents data through pictures or symbols of objects. It helps answer questions about data quickly at a glance without reading detailed tables.

Example: Sleep Duration Survey (Nand Kishor's School)

Scale: 1 Picture Symbol = 10 Children

Response Symbols Calculation Total Children
Always 5 Symbols $5 \times 10$ 50 children
Sometimes 2.5 Symbols $(2 \times 10) + 5$ 25 children
Never 4 Symbols $4 \times 10$ 40 children

4.2.2 Drawing a Pictograph

Lakhanpal collected absenteeism data across different classes:

Class I II III IV V VI VII VIII
Absent Students 3 5 4 2 0 1 5 2

Figure it Out - Exercise Questions

Q1. Data Collection Checklist (Pari's Activity)
  • a. What is the most popular TV show among her classmates? 👉 [✔ Need Data Collection]
  • b. When did India get independence? 👉 [X No Data Collection Needed - Fixed Fact]
  • c. How much water is getting wasted in her locality? 👉 [✔ Need Data Collection]
  • d. What is the capital of India? 👉 [X No Data Collection Needed - Fixed Fact]
Q2. Sweets Shop Selection Summary
  • a. How many students chose jalebi? 6 students
  • b. Barfi was chosen by 3 students.
  • c. How many students chose gujiya? 7 students
  • d. Rasgulla was chosen by 5 students.
  • e. How many students chose gulab jamun? 9 students