Statistics - Mathematics III (PDE, Probability & Statistics)
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Statistics

Statistics

The chapter covers essential concepts in statistics, including measures of central tendency, various probability distributions, correlation and regression methods, tests of significance, and chi-square tests. It emphasizes the application of statistical methods to analyze data and make inferences. Key statistical tools and formulas are provided throughout to support understanding and application.

25 sections

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Sections

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  1. 1
    Basic Statistical Measures

    This section introduces fundamental statistical measures, including measures...

  2. 1.1
    Measures Of Central Tendency

    This section introduces the three primary measures of central tendency:...

  3. 1.2

    This section focuses on the concept of moments in statistics, particularly...

  4. 1.3

    Skewness measures the asymmetry of a probability distribution, indicating...

  5. 1.4

    Kurtosis measures the tailedness or the shape of the data distribution's tails.

  6. 2
    Key Discrete And Continuous Distributions

    This section covers key discrete and continuous probability distributions,...

  7. 2.1
    Binomial Distribution

    The binomial distribution is a discrete probability distribution that...

  8. 2.2
    Poisson Distribution

    The Poisson Distribution describes the probability of a given number of...

  9. 2.3
    Normal Distribution

    The normal distribution is a fundamental statistical concept characterized...

  10. 2.4
    Evaluation Of Parameters

    This section focuses on evaluating key statistical parameters such as mean,...

  11. 3
    Correlation And Regression

    This section focuses on correlation and regression, methods for analyzing...

  12. 3.1
    Pearson Correlation Coefficient

    The Pearson Correlation Coefficient measures the linear relationship between...

  13. 3.2
    Rank Correlation (Spearman's)

    This section introduces Spearman's rank correlation coefficient, a...

  14. 3.3
    Linear Regression

    Linear regression is a statistical method used to model the relationship...

  15. 4
    Curve Fitting By Least Squares

    This section covers curve fitting techniques, specifically focusing on...

  16. 4.1
    Fitting A Straight Line

    This section discusses the method of fitting a straight line to a set of...

  17. 4.2
    Fitting A Parabola

    This section covers the mathematical approach to fitting a parabola using a...

  18. 4.3
    General Curve Fitting

    This section introduces general curve fitting techniques used to approximate...

  19. 5
    Tests Of Significance (Large Samples)

    This section covers various tests of significance applicable to large...

  20. 5.1
    Proportion Tests

    This section introduces proportion tests, essential for analyzing...

  21. 5.2

    This section covers the statistical methods for conducting mean tests...

  22. 5.3
    Standard Deviation Test

    The Standard Deviation Test is a statistical method used to assess...

  23. 6
    Chi-Square Tests

    Chi-Square Tests are statistical methods used to determine the relationship...

  24. 6.1
    Goodness Of Fit

    The goodness of fit test measures how well observed data fits with expected...

  25. 6.2
    Test For Independence

    The Test for Independence evaluates the relationship between two categorical...

What we have learnt

  • Mean, median, and mode are critical for understanding data distribution.
  • Different distributions such as Binomial, Poisson, and Normal have distinct characteristics and formulas.
  • Correlation and regression techniques enable the analysis of relationships between variables.

Key Concepts

-- Mean
The average value of a dataset, calculated as the sum of all values divided by the number of values.
-- Median
The middle value in a dataset when the values are arranged in order.
-- Mode
The value that appears most frequently in a dataset.
-- Skewness
A measure of the asymmetry of the probability distribution of a real-valued random variable.
-- Kurtosis
A statistical measure that describes the shape of a distribution's tails in relation to its overall shape.
-- Binomial Distribution
A distribution that describes the number of successes in a fixed number of independent Bernoulli trials.
-- Correlated Coefficient
A measure that describes the strength and direction of a linear relationship between two variables.
-- ChiSquare Test
A statistical test to determine if there is a significant association between categorical variables.

Additional Learning Materials

Supplementary resources to enhance your learning experience.