Topics
Linear equations in two variables
 Linear Equation in Two Variables
 Simultaneous Linear Equations
 Elimination Method
 Substitution Method
 Cross  Multiplication Method
 Graphical Method of Solution of a Pair of Linear Equations
 Determinant of Order Two
 Cramer’s Rule
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
Quadratic Equations
 Quadratic Equations
 Roots of a Quadratic Equation
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 Formula for Solving a Quadratic Equation
 Nature of Roots of a Quadratic Equation
 The Relation Between Roots of the Quadratic Equation and Coefficients
 To Obtain a Quadratic Equation Having Given Roots
 Application of Quadratic Equation
Arithmetic Progression
 Introduction to Sequence
 Terms in a sequence
 Arithmetic Progression
 General Term of an Arithmetic Progression
 Sum of First ‘n’ Terms of an Arithmetic Progressions
 Arithmetic Progressions Examples and Solutions
 Geometric Progression
 General Term of an Geomatric Progression
 Sum of the First 'N' Terms of an Geometric Progression
 Geometric Mean
 Arithmetic Mean  Raw Data
 Concept of Ratio
Financial Planning
Probability
 Probability  A Theoretical Approach
 Basic Ideas of Probability
 Random Experiments
 Outcome
 Equally Likely Outcomes
 Sample Space
 Event and Its Types
 Probability of an Event
 Type of Event  Elementry
 Type of Event  Complementry
 Type of Event  Exclusive
 Type of Event  Exhaustive
 Concept Or Properties of Probability
 Addition Theorem
Statistics
 Tabulation of Data
 Inclusive and Exclusive Type of Tables
 Ogives (Cumulative Frequency Graphs)
 Applications of Ogives in Determination of Median
 Relation Between Measures of Central Tendency
 Introduction to Normal Distribution
 Properties of Normal Distribution
 Concepts of Statistics
 Mean of Grouped Data
 Method of Finding Mean for Grouped Data: Direct Method
 Method of Finding Mean for Grouped Data: Deviation Or Assumed Mean Method
 Method of Finding Mean for Grouped Data: the Step Deviation Method
 Median of Grouped Data
 Mode of Grouped Data
 Concept of Pictograph
 Presentation of Data
 Graphical Representation of Data as Histograms
 Frequency Polygon
 Concept of Pie Graph (Or a Circlegraph)
 Interpretation of Pie Diagram
 Drawing a Pie Graph
Definition
Arithmetic Mean: The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.
`"Mean" = "Sum of all observations"/"number of observations"`.
Notes
Arithmetic Mean:
 Arithmetic mean is one of the representative values of data.

The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.

It is denoted by the symbol x, read as `bar x`.

The average or Arithmetic Mean (A.M.) or simply mean is defined as follows:
`"Mean" = "Sum of all observations"/"number of observations"`
Example
Two vessels contain 20 liters and 60 liters of milk respectively. What is the amount that each vessel would have if both share the milk equally?
The average or the arithmetic mean would be
= `"Total quantity of milk"/"Number of vessels"`
= `(20 + 60)/2` litres
= 40 litres.
Thus, each vessel would have 40 liters of milk.
Example
Ashish studies for 4 hours, 5 hours, and 3 hours respectively on three consecutive days. How many hours does he study daily on average?
The average study time of Ashish would be
`"Total number of study hours"/"Number of days for which he studied" = (4 + 5 + 3)/3` hours = 4 hours per day
Thus, we can say that Ashish studies for 4 hours daily on an average.
Example
A batsman scored the following number of runs in six innings: 36, 35, 50, 46, 60, 55. Calculate the mean runs scored by him in an inning.
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282.
To find the mean, we find the sum of all the observations and divide it by the number of observations.
Therefore, in this case, mean = `282/6` = 47.
Thus, the mean runs scored in an inning is 47.