Topics
Sets and Relations
- Basics of Relations & Functions
- Representation of a Set
- Intervals
- Classification of Sets
- Relations of Sets
Functions
- Domain and Range of a Function
- Types of Functions
- Representation of Function
- Representation of Function
- Fundamental Functions
- Algebra of Functions
- Composite Function
- Inverse Functions
- Some Special Functions
Complex Numbers 33
- Introduction of Complex Number
- Imaginary Number
- Concept of Complex Numbers
- Conjugate of a Complex Number
- Algebraic Operations of Complex Numbers
- Square Root of a Complex Number
- Solution of a Quadratic Equation in Complex Number System
- Cube Root of Unity
Sequences and Series
- Sequence, Series, and Progression
- Geometric Progression (G. P.)
- General Term Or the nth Term of a G.P.
- Sum to' n' Terms of a Geometric Progression
- Sum to' n' Terms of a Geometric Progression
- Recurring Decimals
- Harmonic Progression (H. P.)
- Types of Means
- Special Series (Sigma Notation)
Locus and Straight Line
- Locus
- Line
- Equations of Lines in Different Forms
- Equations of Line in Different Forms
Determinants
- Determinant of a Matrix
- Properties of Determinants
- Application of Determinants
- Determinant Method (Cramer’s Rule)
- Consistency of Three Linear Equations in Two Variables
- Area of a Triangle Using Determinants
- Collinearity of Three Points
Limits
- Definition of Limit of a Function
- Algebra of Limits
- Evaluation of Limits
- Direct Method
- Methods to Find Limit of Rational Function>Factorization Method
- Methods to Find Limit of Rational Function> Rationalization Method
- Limits of Exponential and Logarithmic Functions
Continuity
- Continuous and Discontinuous Functions
- Examples of Continuous Functions Whereever They Are Defined
Differentiation
- The Meaning of Rate of Change
- Concept of Differentiability
- Derivative by the Method of First Principle
- Rules of Differentiation (Without Proof)
- Applications of Derivatives
Partition Values
- Partition Values
- Deciles
- Percentiles
- Relations Among Quartiles, Deciles and Percentiles
- Graphical Location of Partition Values
Measures of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Measures of Dispersion > Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
Skewness
- Skewness
- Asymmetric Distribution (Positive Skewness)
- Asymmetric (Negative Skewness)
- Measures of Skewness
- Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
- Features of Pearsonian Coefficient
- Bowley’s Coefficient of Skewness
Bivariate Frequency Distribution and Chi Square Statistic
- Bivariate Frequency Distribution
- Classification and Tabulation of Bivariate Data
- Marginal Frequency Distributions
- Conditional Frequency Distributions
- Categorical Variables
- Contingency Table
- Chi-Square Statistic ( χ2 )
Correlation
- Correlation
- Concept of Covariance
- Properties of Covariance
- Concept of Correlation Coefficient
- Scatter Diagram
- Interpretation of Value of Correlation Coefficient
Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Permutations
- Circular Permutations
- Combination
Probability
- Concept of Probability
- Elementary Types of Events and Properties of Probability
- Elementary Properties of Probability
- Addition Theorem of Probability
- Conditional Probability
- Multiplication Theorem of Probability
- Independent Events
Linear Inequations
- Linear Inequations
- Method of Solving a Linear Inequality
- Representation of Inequalities
- Graphical Solution of Linear Inequality of Two Variable
- Solution of System of Linear Inequalities in Two Variables
Commercial Mathematics
- Percentage
- Profit and Loss
- Simple and Compound Interest (Entrance Exam)
- Concept of Depreciation
- Partnership
- Shares
Definition: Quartile
The observations which divide the whole set of observations into four equal parts are known as quartiles.
Before finding quartiles, the given data must always be arranged in ascending order of magnitude.
Definition: Range
The difference between the largest and smallest values in a data set is called the range.
Range = Largest value − Smallest value
Formula: Quartiles
Case I: When n is ODD
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Lower Quartile, Q₁ = (n + 1) / 4 th term
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Upper Quartile, Q₃ = 3(n + 1) / 4 th term
Case II: When n is EVEN
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Lower Quartile, Q₁ = n / 4 th term
-
Upper Quartile, Q₃ = 3n / 4 th term
Formula: Range
Inter-quartile range:
The difference between the upper quartile (Q₃) and the lower quartile (Q₁) is called the inter-quartile range.
Inter-quartile range = Q₃ − Q₁
-
It is always positive, since Q₃ > Q₁.
Semi-interquartile range:
Half of the inter-quartile range is called the semi-interquartile range.
Semi-interquartile range = `1/2` (Q₃ − Q₁)
Key Points: Quartiles and Range in Statistics
Types of Quartiles
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Lower Quartile (Q₁)
The observation lies midway between the lowest value and the median. -
Middle Quartile (Q₂)
The median of the data. -
Upper Quartile (Q₃)
The observation lies midway between the median and the highest value.
