Data Handling Chapter Notes | Mathematics Class 6 ICSE PDF Download

Introduction

Data is all around us, like a treasure chest of information waiting to be explored! From teachers tracking student progress to doctors noting patient details, data helps us understand patterns, make decisions, and plan for the future. Imagine it as a way to organize the world’s stories in numbers, pictures, or charts. In this chapter, we’ll dive into how to collect, organize, and represent data using tools like tally marks, pictographs, and bar graphs, and learn how to find central values like mean and median to summarize data in a meaningful way.

Data

• Data is a collection of information, usually in the form of numbers, that helps us understand and make decisions.
• It’s used by teachers (student records), doctors (patient health), police (crime data), and weather departments (forecasts).
• Data can be organised and shown in different ways, like tables or graphs, to make it easier to understand.

Collecting Data

• Collecting data means gathering information systematically, like asking people questions or recording observations.
• Grouping similar data together makes it easier to count and analyse.
• Steps to Collect Data:
  1. Identify what information you need (e.g., favourite destinations).
  2. Ask or observe to gather responses.
  3. Group similar responses to simplify counting.

Example: A teacher asks students to choose a trip destination. The class monitor groups students by their choices (e.g., Kashmir, Manali) to count how many prefer each place. Grouping helps count faster and avoid mistakes.

Organizing Data

• Organising data means arranging it clearly, often using tables or tally marks.
• Tally marks represent data: each unit is shown by ‘|’ and a group of 5 by (a crossbar over four lines).
• Steps to Organize Data:
  1. List categories (e.g., destinations).
  2. Mark each response with a tally mark in the correct category.
  3. Count tally marks to find the total for each category.

Example: For the trip destination data, the monitor uses tally marks:
Tally marks make it easy to count students per destination.

Pictograph

• A pictograph uses pictures or symbols to represent data, making it visually appealing.
• Each symbol stands for a specific number, explained in a key.
• Pictographs help compare data quickly and clearly.
• Steps to Create a Pictograph:
  1. Choose a symbol to represent a unit of data.
  2. Draw the correct number of symbols for each category based on the data.
  3. Include a key to explain what each symbol means.

Example: A survey shows students’ favourite fruits:
In a pictograph, each fruit symbol represents 1 student, so Mango has 7 symbols, Apple has 4, and so on.

Bar Graphs

• Bar graphs use rectangular bars to show data, with bar height or length showing the frequency.
• Bars are of equal width and spaced evenly for clarity.
• Steps to Construct a Bar Graph:
  1. Draw two perpendicular lines: one horizontal (x-axis), one vertical (y-axis).
  2. Choose a scale (e.g., 1 unit = 2000 bicycles) for the axis showing numerical values.
  3. Draw bars of equal width, with heights matching the data according to the scale.
• Properties of Bar Graphs:
  • Bars can be horizontal or vertical.
  • Bar height or length shows the data value.
  • All bars have the same width for consistency.
  • Equal spacing between bars makes the graph clear.
  • Bars can be shaded or colored for visual appeal.

Example: Number of students present in a class during a week:
A bar graph shows bars for each day, with heights matching the number of students (e.g., 50 for Monday).

Measures of Central Tendency

• Central tendencies are single values that represent the centre of a data set.
• The three types are mean, median, and mode, each summarising data differently.

Arithmetic Mean

• The arithmetic mean (or average) is the sum of all data values divided by the number of values.
• Formula: Mean = (Sum of all observations) / (Total number of observations)
• Steps to Calculate Mean:
  1. Add all the data values.
  2. Count the number of values.
  3. Divide the sum by the count.

Median

• The median is the middle value when data is arranged in order.
• It’s not affected by extreme values, unlike the mean.
• Steps to Calculate Median:
  1. Arrange data in ascending or descending order.
  2. If the number of observations (n) is odd, median is the ((n + 1) / 2)^th value.
  3. If n is even, median is the average of (n / 2)^th and ((n / 2) + 1)^th values.
• Formula:
  • For odd n: Median = ((n + 1) / 2)^th observation
  • For even n: Median = [(n / 2)^th observation + ((n / 2) + 1)^th observation] / 2

Solved Examples

Example 1: Organising Data
In a Mathematics test, marks of 40 students are given. Arrange in a table using tally marks and find: 
(a) students with 8 or more marks, (b) students with less than 4 marks, (c) students with the highest marks.
Solution:(a) 8 or more marks: 3 (8) + 4 (9) = 7 students.
(b) Less than 4 marks: 4 (1) + 2 (2) + 3 (3) = 9 students.
(c) Highest marks (9): 4 students.

Example 2: Pictograph
Number of cows in five villages: 
A (70), B (100), C (80), D (60), E (50). 
Create a pictograph using a circle for 10 cows and answer:
 (a) symbols for village A, 
(b) village with maximum cows, 
(c) difference between A and D, 
(d) represent 35 cows.
Solution:(a) Village A: 70 ÷ 10 = 7 circles.
(b) Village B has the maximum (100 cows).
(c) A (70) - D (60) = 10 cows.
(d) 35 cows = 3 full circles and 1 half circle.

Example 3: Bar Graph
Bicycles manufactured from 2014 to 2018: Use scale 1 unit = 2000 bicycles. Find: 
(a) year with maximum bicycles, 
(b) year with minimum bicycles.
Solution: Draw bars with heights: 2014 (1.5 units), 2015 (1 unit), 2016 (3 units), 2017 (5.5 units), 2018 (6.5 units).(a) 2018 (13000 bicycles).
(b) 2015 (2000 bicycles).