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Introduction to Mathematical Statistics

Need help in Math Statistics?

What is Math Statistics? The study of math statistics includes the collection, analysis, presentation and interpretation of data. When data is collected, summarized and represented as graphs, we can look for trends and try to make predictions based on these facts.

This series of lessons will cover: Collecting and summarizing data, Common ways to describe data, Different ways to represent data, Frequency Tables, Cumulative Frequency, More advanced Statistics, Descriptive Statistics, Probability, Correlation, and Inferential Statistics

A. Collecting and summarizing data

Data Frequency and Frequency Tables

B. Common ways to describe data

Mode Median
Mean Range

C. Different ways to represent data

Tally Charts and Line Plots Pictograms / Pictographs
Bar Charts Line Graphs
Pie Charts / Pie Graphs / Circle Graphs Box and Whiskers Plot
Stem-and-Leaf Plot Venn Diagrams
Carroll Diagrams

D. Frequency Tables

Frequency Tables Frequency Table with Intervals
Mode and Mean from Frequency Table Mean from Frequency Table with Intervals
Median from Frequency Table Histogram with Uniform Widths
Histogram with Non-Uniform Widths  

E. Cumulative Frequency

Cumulative Frequency Table Cumulative Frequency Graph
Median, Quartiles, Percentiles (Ungrouped Data) Median, Quartiles, Percentiles (Grouped Data)

F. More Advanced Statistics

Population Mean and Sample Mean Population Variance & Sample Variance
Standard Deviation Random Variable
Probability Density Functions Binomial Distribution
Expected Value Poisson Distribution
Normal Distribution Z-Score
Bayes' Theorem Normal Probability Plot Videos
Confidence Interval Videos Chi-Square Test Videos
ANOVA Test Central Limit Theorem videos
Sampling Distribution videos Logistic Equations videos
Chebychev's Theorem videos  


A series of free Statistics Lectures in videos

Descriptive Statistics

The Basics: Descriptive and Inferential Statistics
Sampling Methods
Types of Variables
Independent and Dependent Variables
Variable Measurement Scales
Frequency Distributions and Cumulative Frequency Distributions
Bar Graphs and Pie Charts
Histograms and Stem & Leaf Plots
Arithmetic Mean for Samples and Populations
Central Tendency: Mean, Median, and Mode
Variance and Standard Deviation of a Population
Variance and Standard Deviation of a Sample
Percentiles and Quartiles
The Five Number Summary, Interquartile Range (IQR), and Boxplots
The Effects of Outliers
The Normal Curve and Empirical Rule
Extra Z-Score Problems

The Basics of Probability
Addition Rule (Probability "or")
Multiplication Rule (Probability "and")
Discrete and Continuous Random Variables
Discrete Probability Distributions
Probability Histograms
Mean and Expected Value of Discrete Random Variables
Variance and Standard Deviation of Discrete Random Variables
The Law of Large Numbers
Binomial Distribution
Mean and Standard Deviation of Binomial Random Variables
Poisson Distribution/Process
Mean and Standard Deviation of Poisson Random Variables
Bernoulli Distribution
Scatter Plots
Pearson's r Correlation
Hypothesis Testing with Pearson's r
Linear Regression
Spearman Correlation
Correlation vs. Causation

Inferential Statistics
Parameters, Statistics, and Sampling Error
Distribution of the Sample Mean
The Central Limit Theorem
Sample Proportions
Confidence Intervals about the Mean, Population Standard Deviation Known
Calculating Required Sample Size to Estimate Population Mean
Student's t-Distribution
Confidence Intervals about the Mean
Population Standard Deviation Unknown
Confidence Intervals for Population Proportions
Calculating Required Sample Size to Estimate Population Proportions
Null and Alternative Hypotheses
Type I and Type II Errors
One-Tailed and Two-Tailed Tests
Effect Size
Statistical vs. Practical Significance
Independent and Dependent Samples
One Sample z-Test
One Sample z-Test for Proportions
One Sample t-Test
Independent Samples t-Test
Confidence Intervals for Independent Samples t-Test
Effect Size for Independent Samples t-Test
Dependent Samples t-Test
Confidence Intervals for Dependent Samples t-Test
Effect Size for Dependent Samples t-Test
z-Test for Proportions, Two Samples
Confidence Intervals for the Difference of Two Proportions
Introduction to ANOVA
Effect Size for One-Way ANOVA
Post-Hoc Tests for One-Way ANOVA
Repeated-Measures ANOVA
Factorial ANOVA, Two Independent Factors
Factorial ANOVA, Two Dependent Factors
Factorial ANOVA, Two Mixed Factors
Chi-Square Test for Goodness of Fit
Chi-Square Test for Independence
Mann-Whitney U-Test
Wilcoxon Signed-Ranks Test
The Kruskal-Wallis Test
The Friedman Test

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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