# Describing Univariate Data

Type of data: categorical vs. numerical, continuous vs. discrete.
• ## Numerical Summaries

• ### Measuring Location (Center)

Three most commonly used measure of center: mean, median and mode.
Percentiles. Quartiles (1st quartile = Q1, 3rd quartile = Q3).
Extremes: minimum and maximum.
The median, upper and lower quartiles, minimum and maximum are collectively called the five-number summary.
Z-score: How to compute it? What does it mean?

Most commonly used: variance, standard deviation (square-root of variance), inter-quartile range (IQR), range (max-min).

• ### Properties

Shapes of distribution: symmetric, skewed left or skewed-right.
Unimodal: has a single peak.
Tails: long tailed (many outliers) or short tailed (few outliers).
When are median and IQR preferable to mean and variance: outliers present, or distribution skewed.
Empirical Rule: what does it say? What assumption(s) do you need to use it?
Chebychev's Rule: what does it say? What assumption(s) do you need to use it?

• ## Graphical Summary

Stem-and-leaf display: How to construct it? What does it show? Advantages and disadvantages?
Boxplot: How to construct it? What does it show? Advantages and disadvantages?
Normal quantile plot: What does it show?

# Bivariate Data

Numerical Summaries:
Pearson's correlation coefficient: what does it measure? when is it applicable? what values can it take on?
Spearman's rank correlation coefficient: what is it? why use it?
Least Squares line: what is it? what's the relationship with correlation coefficient? what does the intercept and slope mean?
Coefficient of determination: What is it? what does it mean? what values can it take on?
Graphical Summaries: scatterplot.

# Basic Probability

• ## Basic Definitions

Definition (or meaning of) sample space, event, random experiment, union, intersection, complement, mutually exclusive, random variable, expected value.
The three basic rule of probability.
Conditional probability: what does it mean?
The difference between mutually exclusive and independent.

• ## Discrete Distributions

What are the situations/setup for the following distributions: binomial, hypergeometric, negative binomial, Poisson.
The difference between sampling with and without replacement.

# Normal Distribution, Sampling Distribution of a Statistic

• ## Normal distribution

How does a generic normal distribution relate to the standard normal distribution?

• ## Sampling Distributions

Definitions: population, random sample, parameter, statistic, sampling distributions.
Basic situations for statistical inference: what are the parameters and corresponding statistics?
Sampling from one, two or several continuous populations.
Sampling from one, two or several 0-1 populations.
Paired data.
Simple linear regression and correlation.

• ## Central Limit Theorem

What does it say? What does it assume?
Normal approximation to the binomial probabilities: an application of the CLT.

• ## Transformed Statistics

A transformed statistic measures how close a statistic is to the corresponding parameter. The sampling distribution of a transformed statistic tells us how likely for a random sample to yield a statistic with the value we got from our particular sample.