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Statistics Topics

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Graphing Data

Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Reading and drawing Venn diagrams
Stem and leaf plots
Advantages and disadvantages of different graphs (free lessons)
Misleading graphs
Critiquing data presentation
Frequency distribution and histograms
Frequency polygons
Shapes of distributions

Designing Studies

Influencing factors in data collection (free lessons)
Data collection
Classification of data
Sampling methods
Census and bias

Measures of Central Tendency

Median and mode
Mean
Range and outliers
Application of averages
Center of a data set: mean, median, mode

Measures of Dispersion

Spread of a data set - standard deviation & variance
Measures of relative standing - z-score, quartiles, percentiles

Discrete Probabilities

Probability distribution - histogram, mean, variance & standard deviation
Binomial distribution
Mean and standard deviation of binomial distribution
Poisson distribution
Geometric distribution
Negative binomial distribution
Hypergeometric distribution
Properties of expectation

Normal Distribution and Z-Scores

Introduction to normal distribution
Normal distribution and continuous random variable
Z-scores and random continuous variables
Sampling distributions
Central limit theorem
Rare event rule

Confidence Intervals

Point estimates
Confidence levels and critical values
Margin of error
Making a confidence interval
Confidence intervals to estimate population mean
Student's t-distribution
Chi-Squared confidence intervals

Bivariate Data

Bivariate, scatter plots and correlation
Regression analysis
Equation of the best fit line

Permutations and Combinations

Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Probability involving permutations and combinations

Probability

Introduction to probability
Organizing outcomes
Probability of independent events
Comparing experimental and theoretical probability
Determining probabilities using tree diagrams and tables (free lessons)
Probability of independent events
Probability
Addition rule for "OR"
Multiplication rule for "AND"
Conditional probability
Law of total probability
Bayes' rule
Probability with Venn diagrams

Hypothesis Testing

Null hypothesis and alternative hypothesis
Proving claims
Confidence levels, significance levels and critical values
Test statistics
Traditional hypothesis testing
P-value hypothesis testing
Mean hypothesis testing with t-distribution
Type 1 and type 2 errors
Chi-Squared hypothesis testing
Analysis of variance (ANOVA)
Chi-square goodness of fit test
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