Topics
Sets and Relations
- Concept of Relations
- Representation of a Set
- Intervals
- Classification of Sets
- Relations of Sets
Functions
- Concept of 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
- Concept of Determinant
- Properties of Determinants
- Application of Determinants to Coordinate Geometry
- Methods of Solving Linear Equations in Two Variables > Determinant method (Cramer’s Rule)
- Consistency of Three Linear Equations in Two Variables
- Application of Determinants to Coordinate Geometry
- 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
Linear Inequations
Commercial Mathematics
- Percentage
- Profit and Loss
- Simple and Compound Interest (Entrance Exam)
- Concept of Depreciation
- Partnership
- Shares
bivariate data, tabulation of bivariate data
Video Tutorials
Shaalaa.com | Frequency Distribution
to track your progress
Related QuestionsVIEW ALL [18]
Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.
| X | 27 | 25 | 28 | 26 | 29 | 27 | 28 | 26 | 25 | 25 | 27 |
| Y | 21 | 20 | 20 | 21 | 23 | 22 | 20 | 20 | 19 | 19 | 23 |
| X | 26 | 29 | 25 | 27 | 26 | 25 | 28 | 25 | 27 | 26 | |
| Y | 19 | 23 | 23 | 22 | 21 | 20 | 22 | 23 | 22 | 21 |
Find conditional frequency distribution of age of husbands when the age of wife is 23 years.
Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).
| Marks in Statistics (X) |
37 | 20 | 46 | 28 | 35 | 26 | 41 | 48 | 32 | 23 | 20 | 39 | 47 | 33 | 27 | 26 |
| Marks in English (Y) |
30 | 32 | 41 | 33 | 29 | 43 | 30 | 21 | 44 | 38 | 47 | 24 | 32 | 21 | 20 | 21 |
Construct a bivariate frequency distribution table for the above data by taking class intervals 20 – 30, 30 – 40, ...... etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between 30 – 40.
Related concepts
- Concepts of Statistics - Comparison of Two Frequency Distributions with Same Mean
- Concepts of Statistics - Co-efficient of Variation
- Concepts of Statistics - Effect of Change of Origin and Scale on Variance and Standard Deviation
- Concepts of Statistics - Combined Variance and Standard Deviation
