Topics
Number System (Including Estimation and Approximation)
Number System
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Ratio and Proportion
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Estimation
Theme 3 : Algebra
Numbers in India and International System (With Comparison)
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Place Value
Negative Numbers and Integers
Geometry
Theme 4 : Geometry
Mensuration
Theme 5 : Mensuration
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Theme 6 : Statistics
Data Handling
Fractions
Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Sets
Percent (Percentage)
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Fundamental Concepts (Including Angles and their Properties)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Triangles (Including Types and Properties of Triangles)
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Recognition of Solids
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Data Handling (Including Mean and Median)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Definition: Mean (or Average)
- Formula: Average
- Example 1
- Example 2
- Types of Averages
Introduction
In our daily lives, we often need to find a single number that represents an entire group of numbers. For example:
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Sports: When we say Virat Kohli's average score in one-day internationals is 86, we mean that if we add all the runs he scored and divide by the number of matches, we get 86 runs per match.
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School: Your class average marks tell you how well the entire class performed overall.
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Income: Average salary helps us understand what a typical employee earns in a company.
Definition: Mean (or Average)
The term Mean (or Average) refers to a single, representative value that is used to summarize an entire set of data. Its main purpose is to locate the "center" or typical value within a data distribution.
Mathematically, an average is known as a Measure of Central Tendency.
Formula: Average
Mean (or Average) = `"Sum of all observations" / "Total number of observations"`
Example 1
Question: If 5 employees earn ₹20,000, ₹25,000, ₹30,000, ₹22,000, and ₹28,000 respectively, what is the average income?
Solution:
Average = `"Sum of all observations" / "Total number of observations"`
Average income = `"(20,000 + 25,000 + 30,000 + 22,000 + 28,000)" / 5`
= `"125,000" / 5`
= ₹25,000.
Example 2
Question: Find the value of x if the mean of 10, 12, 13, x, and 17 is 14.
Solution:
Mean = `"Sum of data"/"Number of data"`
⇒ 14 = `"10 + 12 + 13 + x + 17"/"5"`
⇒ 14 = `"52 + x"/ 5`
⇒ 70 = 52 + x and x = 70 − 52 = 18
Types of Averages
Mathematicians have identified three main useful measures to find the average of a set of data:
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Mean (Arithmetic Average)
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Median (Middle Value)
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Mode (Most Common Value)
