Data Handling — Class 6 Mathematics

'Data is everywhere — from the marks in your class to the rainfall in Andhra Pradesh. Learning to read it is a superpower.'

1. Introduction

Data is a collection of facts and information. In everyday life, we encounter data constantly — test scores, cricket scores, temperatures, prices. Data handling is the skill of collecting, organising, presenting, and interpreting this information.

Why This Chapter Matters

• Foundation for statistics in higher classes
• Used in science, economics, business
• Helps make decisions based on evidence
• AP context: analysing crop yields, rainfall data, exam results

2. Recording and Organising Data

Raw Data

Unorganized data is called raw data.

Example: The favourite fruits of 20 students in a class: Mango, Apple, Banana, Mango, Orange, Apple, Mango, Banana, Mango, Apple, Banana, Orange, Mango, Mango, Apple, Banana, Mango, Orange, Apple, Mango

This is hard to read! We need to organise it.

Frequency Distribution Table

A table showing how often each item occurs.

'Organising data makes patterns visible. A frequency table is the first step to understanding data.'

Steps to Create a Frequency Table

1. List all distinct items/categories
2. Go through raw data one by one
3. Mark a tally for each occurrence
4. Count tallies and write frequency
5. Add frequencies to check total

3. Tally Marks

Tally marks are a quick way to record and count frequencies.

How to Record Tallies

• Count 1: |
• Count 2: ||
• Count 3: |||
• Count 4: ||||
• Count 5: |||| (the fifth mark crosses the first four)
• Count 6: |||| |
• Count 10: |||| ||||
• Count 15: |||| |||| ||||

Grouping by Fives

Tallies are grouped in sets of five for easy counting. The fifth mark goes diagonally across the previous four.

1: |
2: ||
3: |||
4: ||||
5: |\cancel{||||}  (or +)
6: |\cancel{||||} |

'Always group tallies in fives. This makes counting by fives quick and reduces errors.'

4. Pictographs

A pictograph uses pictures or symbols to represent data. Each picture stands for a certain number of items.

Example: Number of Books Read

Scale: Each 📖 = 2 books

Reading Pictographs

Ravi: 4 📖 × 2 = 8 books Sita: 3 📖 × 2 = 6 books Gopal: 5 📖 × 2 = 10 books Laxmi: 2 📖 × 2 = 4 books

Rules for Drawing Pictographs

1. Choose a simple, clear symbol
2. Decide on a SCALE (what each symbol represents)
3. The scale should be a convenient number (1, 2, 5, 10, 50, 100)
4. Use half-symbols for values that don't fit exactly
5. Always write the scale clearly
6. Give the pictograph a title

Scale Selection Guide

Worked Example: AP Mango Production

Scale: 🥭 = 100 tonnes

Create pictograph: Krishna: 🥭🥭🥭🥭🥭 (500) Guntur: 🥭🥭🥭 (300) Chittoor: 🥭🥭🥭🥭 (400) E. Godavari: 🥭🥭 (200)

5. Bar Graphs

A bar graph represents data using rectangular bars of equal width. The height (or length) of each bar is proportional to the value it represents.

Parts of a Bar Graph

• Title: What the graph is about
• X-axis (horizontal): Categories/items
• Y-axis (vertical): Values/frequencies
• Bars: Equal width, separated by equal gaps
• Scale: On the Y-axis

Reading a Bar Graph

Example: Marks scored by 5 students

Marks →
100 |       ██
 90 |       ██  ██
 80 |  ██   ██  ██  ██
 70 |  ██   ██  ██  ██  ██
 60 |  ██   ██  ██  ██  ██
 50 |  ██   ██  ██  ██  ██
    +-------------------------→
      Ram  Ravi  Sita  Gita  Tom

From the graph:

• Ram scored 60
• Ravi scored 80
• Sita scored 100 (highest)
• Gita scored 75
• Tom scored 50 (lowest)

Drawing a Bar Graph — Step by Step

Problem: Draw a bar graph for the favourite colours of 30 students.

Steps:

1. Draw X-axis and Y-axis
2. Label X-axis: 'Colour' — write Red, Blue, Green, Yellow, Pink at equal intervals
3. Label Y-axis: 'Number of Students' — choose scale: 1 unit = 2 students
4. Mark Y-axis from 0 to 10 (or 0 to 12)
5. Draw bars of equal width for each colour:
   • Red: height = 8 units (4 divisions)
   • Blue: height = 10 units (5 divisions)
   • Green: height = 5 units (2.5 divisions)
   • Yellow: height = 4 units (2 divisions)
   • Pink: height = 3 units (1.5 divisions)
6. Give the graph a title: 'Favourite Colours of Class 6 Students'

Choosing the Scale

• Ensure the largest value fits on the Y-axis
• Choose divisions that are easy to read (1, 2, 5, 10, 20, 50, 100)
• If data is 5, 12, 8, 15: scale 1 unit = 2 works well
• If data is 50, 120, 80: scale 1 unit = 10 or 20

Bar Graph vs Pictograph

6. Interpretation of Data

What to Look For

1. Highest/Maximum: The category with the tallest bar
2. Lowest/Minimum: The category with the shortest bar
3. Comparison: How categories compare to each other
4. Total: Sum of all values
5. Difference: Difference between any two categories

Worked Example: Rainfall in AP Districts (mm)

Interpretation:

• Highest rainfall: Srikakulam (1200 mm)
• Lowest rainfall: Anantapur (500 mm)
• Difference between highest and lowest: 1200 − 500 = 700 mm
• Coastal districts receive more rainfall than Rayalaseema districts

7. Worked Problems

Problem 1 (Tally Marks)

The birthdays of 25 students fall in these months: Jan, Mar, Jan, Apr, Jan, Feb, Mar, Jan, Feb, Mar, Apr, Jan, Feb, Mar, Jan, Apr, Jan, Mar, Feb, Jan, Mar, Apr, Jan, Feb, Jan

Make a frequency table.

Solution:

Problem 2 (Bar Graph)

Draw a bar graph showing the number of different types of trees in a park in Vijayawada: Neem (15), Banyan (8), Peepal (10), Mango (12), Coconut (20).

Solution approach:

• Title: 'Trees in Vijayawada Park'
• X-axis: Tree types (Neem, Banyan, Peepal, Mango, Coconut)
• Y-axis: Number of trees (scale: 1 unit = 2 trees)
• Bars: Neem=15 (7.5 div), Banyan=8 (4 div), Peepal=10 (5 div), Mango=12 (6 div), Coconut=20 (10 div)

8. Common Mistakes — Fix Them Now

9. Exam Focus

Marks Blueprint

Quick Self-Test (5 Questions)

Q1: What does each tally group of five represent?

Q2: In a bar graph, what should be equal for all bars?

Q3: The favourite food of 40 students: Biryani (15), Dosa (10), Pulao (8), Rice (7). Which food is most popular?

Q4: In a pictograph, one symbol = 5 books. How many symbols for 35 books?

Q5: What is the total frequency if tally marks are: |||| ||| and |||| ||||?

10. Chapter Summary

• Data: collection of facts; Raw data: unorganized
• Frequency table: organises data with tallies and counts
• Tally marks: grouped in fives for easy counting
• Pictograph: uses symbols; needs a clear scale
• Bar graph: rectangular bars; X-axis = categories, Y-axis = values
• Scale: pick convenient numbers (1, 2, 5, 10, 50, 100)
• Interpretation: find highest, lowest, differences, totals

'Data handling is not just mathematics — it is the skill of making sense of the world through numbers and pictures.'