STA301 Handouts by VUBuddy

Virtual University of Pakistan ii

TABLE OF CONTENTS · TITLE · PAGE NO

Definition of Statistics Observation and Variable Types of Variables Measurement Sales Error of Measurement

Data collection Sampling

Types of Data Tabulation and Presentation of Data Frequency distribution of Discrete variable

Frequency distribution of continuous variable

Types o frequency Curves Cumulative frequency Distribution

Stem and Leaf Introduction to Measures of Central Tendency Mode

Arithmetic Mean Weighted Mean Median in case of ungroup Data

Median in case of group Data Median in case of an open-ended frequency distribution Empirical relation between the mean, median and the mode Quantiles (quartiles, deciles & percentiles) Graphic location of Quantiles

Geometric mean Harmonic mean Relation between the arithmetic, geometric and harmonic means Some other measures of central tendency

Concept of dispersion Absolute and relative measures of dispersion Range Coefficient of dispersion Quartile deviation Coefficient of quartile deviation

Mean Deviation Standard Deviation and Variance Coefficient of variation

The Empirical Rule The Five-Number Summary Virtual University of Pakistan iii Box and Whisker Plot Pearson’s Coefficient of Skewness

Bowley’s coefficient of Skewness The Concept of Kurtosis Percentile Coefficient of Kurtosis Moments & Moment Ratios Sheppard’s Corrections The Role of Moments in Describing Frequency Distributions

Simple Linear Regression Standard Error of Estimate Correlation

Basic Probability Theory Set Theory Counting Rules: The Rule of Multiplication

Permutations Combinations Random Experiment Sample Space Events Mutually Exclusive Events Exhaustive Events Equally Likely Events

Definitions of Probability Relative Frequency Definition of Probability

Relative Frequency Definition of Probability Axiomatic Definition of Probability Laws of Probability Rule of Complementation Addition Theorem

Application of Addition Theorem Conditional Probability Multiplication Theorem

Independent and Dependent Events Multiplication Theorem of Probability for Independent Events Marginal Probability

Bayes’ Theorem Discrete Random Variable Discrete Probability Distribution Graphical Representation of a Discrete Probability Distribution Mean, Standard Deviation and Coefficient of Variation of a Discrete Probability Distribution Distribution Function of a Discrete Random Variable

Graphical Representation of the Distribution Function of a Discrete Random Variable Mathematical Expectation Mean, Variance and Moments of a Discrete Probability Distribution Properties of Expected Values Virtual University of Pakistan iv Concept of Continuous Probability Distribution Mathematical Expectation, Variance & Moments of a Continuous Probability Distribution

Mathematical Expectation, Variance & Moments of a Continuous Probability Distribution BIVARIATE Probability Distribution

BIVARIATE Probability Distributions (Discrete and Continuous) Properties of Expected Values in the case of Bivariate Probability Distributions

Properties of Expected Values in the case of Bivariate Probability Distributions Covariance & Correlation Some Well-known Discrete Probability Distributions: Discrete Uniform Distribution An Introduction to the Binomial Distribution

Binomial Distribution Fitting a Binomial Distribution to Real Data An Introduction to the Hyper geometric Distribution

Hyper geometric Distribution Poisson distribution and limiting approximation to Binomial Poisson Process Continuous Uniform Distribution

Normal Distribution The Standard Normal Distribution Normal Approximation to the Binomial Distribution

Sampling Distribution of X Mean and Standard Deviation of the Sampling Distribution of X Central Limit Theorem

Sampling Distribution of pˆ

Sampling Distribution of X X 

Point Estimation Desirable Qualities of a Good Point Estimator

Methods of Point Estimation Interval Estimation

Confidence Interval for  Confidence Interval for 1-2

Large Sample Confidence Intervals for p and p1-p2 Determination of Sample Size (with reference to Interval Estimation) Hypothesis-Testing (An Introduction)

Hypothesis-Testing (continuation of basic concepts) Hypothesis-Testing regarding  (based on Z-statistic

Hypothesis-Testing regarding 1 - 2 (based on Z-statistic) Hypothesis Testing regarding p (based on Z-statistic)