Topics
Linear equations in two variables
- Introduction to linear equations in two variables
- Methods of solving linear equations in two variables
- Simultaneous method
- Simultaneous method
- Substitution Method
- Cross - Multiplication Method
- Graphical Method
- Determinant method
- Determinant of Order Two
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Application of simultaneous equations
- Simultaneous method
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 Circle-graph)
- 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.
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The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.
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It is denoted by the symbol x, read as `bar x`.
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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.
