Data Through Pictures

Chapter at a Glance

This chapter covers data handling, focusing on pictographs and bar graphs. Using everyday situations—such as surveying hours spent watching TV, taking stock of toy store inventory, recording traffic counts, tracking daily routines, measuring finger lengths, and auditing canteen food waste—students learn to collect, display, scale, and interpret data.

Key Definitions & Terminology

• Data: A collection of facts, numbers, or measurements gathered through surveys or observations.
• Pictograph: A chart that uses pictures or symbols to represent data quantities.
• Scale: The numeric value represented by a single symbol or icon in a pictograph (e.g. $1 \text{ icon} = 5 \text{ items}$). A scale makes it easier to represent large numbers using fewer drawings.
• Bar Graph: A visual representation of data using vertical or horizontal rectangular bars, where the height or length of each bar represents its value.
• Vertical Axis: The vertical line on a bar graph showing the numeric scale.
• Horizontal Axis: The horizontal line on a bar graph showing categories (e.g. activity names or weekdays).

Formulas, Rules & Properties

• Interpreting Pictographs:
  To calculate the actual count from a pictograph:
  $$\text{Actual Quantity} = \text{Number of Icons} \times \text{Scale Value}$$
• Wasted Food to Children Fed Conversion:
  If $1\text{ kg}$ of wasted food is equivalent to feeding $N$ children:
  $$\text{Children Fed} = \text{Total Wasted Food (in kg)} \times N$$

Core Concepts & Topics

• TV Hours Survey:
• Gathering data from $35$ children on their daily television watching times ($0.5\text{ hr}, 1\text{ hr}, 1.5\text{ hrs}, 2\text{ hrs}, \text{or more}$).
• Joseph Uncle's Store Stock:
• Designing scaled pictographs where one icon represents $5$ items to record inventory of toys, board games, and sports items.
• Traffic Count Logs:
• Using a scale of $1 \text{ icon} = 3 \text{ two-wheelers}$ to record vehicles passing a house on Monday, Wednesday, and Friday.
• Comparing Daily Routines (Raman vs. Sheela):
• Comparing a pictograph routine (Raman) with a bar graph routine (Sheela) to evaluate hours spent sleeping, studying, in school, and playing.
• Finger Length Graphing:
• Pasting paper strips corresponding to index finger lengths onto a grid sheet to create a physical bar graph.
• School Canteen Food Wastage:
• Reading a bar graph showing food waste in kilograms (sandwiches, parathas, khichdi, idli-sambar, etc.) and calculating the potential number of children who could have been fed.
• Visual Observation Analysis:
• Verifying statements (True/False) about characteristics of a group of children (e.g. count of those wearing caps, glasses, holding books, or carrying backpacks).

Worked Examples

• Joseph Uncle's Store Pictograph:
• Scale: $1 \text{ icon} = 5 \text{ items}$.
• Icons recorded: Toys ($6$ icons), Board games ($4$ icons), Sports items ($5$ icons).
• Calculations:
  • Toys $= 6 \times 5 = \mathbf{30 \text{ toys}}$.
  • Board games $= 4 \times 5 = \mathbf{20 \text{ board games}}$.
  • Sports items $= 5 \times 5 = \mathbf{25 \text{ sports items}}$.
  • Total items $= 30 + 20 + 25 = \mathbf{75 \text{ total items}}$.
• Two-Wheelers Road count:
• Scale: $1 \text{ icon} = 3 \text{ two-wheelers}$.
• Icons recorded: Monday ($5$ icons), Wednesday ($3$ icons), Friday ($6$ icons).
• Questions & Solutions:
  1. Which day had the most two-wheelers? Friday ($6 \times 3 = 18$ two-wheelers).
  2. What was the total count recorded? $15 \text{ (Mon)} + 9 \text{ (Wed)} + 18 \text{ (Fri)} = \mathbf{42 \text{ two-wheelers}}$.
  3. How many fewer were seen on Wednesday than Monday? $15 - 9 = \mathbf{6 \text{ fewer}}$.
  4. How many more were seen on Friday than Wednesday? $18 - 9 = \mathbf{9 \text{ more}}$.
• Raman vs. Sheela Daily Routines:
• Raman (1 icon = 1 hour): Sleeping ($8\text{ hr}$), School ($6\text{ hr}$), Studying ($2\text{ hr}$), Playing ($4\text{ hr}$), Others ($4\text{ hr}$).
• Sheela (Bar Graph): Sleeping ($9\text{ hr}$), School ($6\text{ hr}$), Studying ($4\text{ hr}$), Playing ($3\text{ hr}$), Others ($2\text{ hr}$).
• Questions & Solutions:
  1. Who sleeps more? Sheela ($9\text{ hr}$ vs. $8\text{ hr}$).
  2. Who spends more hours in school? Both spend the same time ($6\text{ hours}$ each).
  3. How many more hours does Sheela study than Raman? $4 - 2 = \mathbf{2 \text{ hours}}$.
• Canteen Food Waste:
• Problem: A canteen records the following waste: Monday ($4\text{ kg}$), Tuesday ($3.5\text{ kg}$), Wednesday ($2\text{ kg}$), Thursday ($5\text{ kg}$), and Friday ($3\text{ kg}$). If $1\text{ kg}$ of food can feed $3$ children, how many children could have been fed with the total food wasted?
• Solution:
  1. Total food wasted $= 4 + 3.5 + 2 + 5 + 3 = 17.5\text{ kg}$.
  2. Children who could be fed $= 17.5\text{ kg} \times 3 = \mathbf{52.5 \text{ children}}$ (or $52$ children completely).

Practical Activities & Experiments

• TV Hours Survey: Conducting a classroom survey on television viewing times, compiling the responses in a frequency table, and discussing healthy screen time limits.
• Wind-Gauge / Traffic Log: Counting cars, two-wheelers, and cycles passing the school gate over a 15-minute period and drawing a pictograph using a custom scale.
• Finger Length Strip Graph: Tearing scrap paper strips to match index finger lengths, pasting them on a bar chart axis, and comparing results.
• Canteen Food Waste Audit: Monitoring lunch plates in the school canteen for a week, recording waste weights, and plotting them on a bar graph.