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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

–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 Probabilites

–Probability distribution - histogram, mean, variance & standard deviation

–Binomial distribution

–Mean and standard deviation of binomial

–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

–Scatter plots and Correlations

–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 with 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

–Addition rule for "OR"

–Multiplication rule for "AND"

–Conditional probability

–Laws of total probability

–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

Discrete Probabilites

–Probability distribution - histogram, mean, variance & standard deviation

–Binomial distribution

–Mean and standard deviation of binomial

–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

–Scatter plots and Correlations

–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 with 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

–Addition rule for "OR"

–Multiplication rule for "AND"

–Conditional probability

–Laws of total probability

–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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