Statistics and Probability

Sample Space

Sample Space

A collection of all possible outcomes of a random experiment.

Sample Size

The number of observations or individuals in a sample selected from a larger population.

Discrete Random Variables

A random variable that has either a finite or countable number of values.

Continuous Random Variables

A variable that has infinitely many values.

Sampling Methods

Different techniques used to select samples from a population, including simple, convenience, systematic, quota, and stratified sampling.

Grouped Frequency Distributions

Data grouped into intervals or classes instead of listing each individual data point.

Cumulative Frequency

The running total of frequencies in a frequency distribution.

Cumulative Frequency Curve

A graphical representation of cumulative frequencies.

Correlation

Measures the relationship between two variables and the strength and direction of their association.

Regression

Helps in understanding and modeling the relationship between a dependent variable and one or more independent variables.

Probability Basics

Fundamental rules and concepts in probability theory, including the addition rule, multiplication rule, and complement rule.

Discrete Random Variables (DRVs)

Random variables assigned a probability in random experiments with a finite or countable number of values.

Binomial Distribution

Applies to events that can be described as a "success" or "failure" with a fixed number of trials and a constant probability of success.

Normal Distribution

A bell-shaped probability distribution characterized by its mean and standard deviation.

X on Y Regression

Another way of describing a linear regression.

Conditional Independence

The independence of two random variables given the value of a third random variable.

Normal Standardization

The process of standardizing data to have a mean of 0 and a standard deviation of 1.

Bayes' Theorem

Describes how to update the probability of a hypothesis based on new evidence.

Continuous Random Variables (CRVs)

Random variables that can take on any value within a certain range or interval.

Statistics

A branch of mathematics that involves analyzing and interpreting data.

Mean

The average of a population, calculated by summing all values and dividing by the number of values.

Median

The middle value in a dataset when arranged in ascending or descending order.

Mode

The value that occurs most frequently in a dataset.

Range

The difference between the highest and lowest data values.

Probability

The likelihood of an event occurring, often measured numerically.

Random Experiment

An experiment in which the outcome cannot be determined beforehand.

Trial

An action in a random experiment.

Outcome

A possible result of a trial.

Event

A set of possible outcomes.

Multiplication Rule

Used to calculate the probability of both event A and event B occurring.

Frequency Distributions

A list of each category and the number of occurrences for each category of data.

Standard Deviation

Measures the deviation between scores and the mean, representing the average of differences between values and the mean.

Continuous Random Variables

A variable that has infinitely many values and can be plotted on a line in an uninterrupted fashion.

Binomial Distribution

A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.

Chi-Square

A statistical test that determines whether a set of observed values matches those expected under the applicable model.

Goodness of Fit

A statistical test that determines whether a set of observed values matches those expected under the applicable model.

Cumulative Frequency Distribution

A graph that displays the aggregate frequency of a category or the total number of observations that are less than or equal to the categories.

Cumulative Relative Frequency Distribution

A graph that displays the proportion or percentage of observations that are less than or equal to the categories of the discrete data.

Hypothesis Testing

An assumption about a population parameter that may or may not be true and is tested using sample data.

Alternative Hypothesis (H0)

The belief that a new drug has a different effect on average compared to a current drug or that the new drug is better on average than the current drug.

Null Hypothesis (H1)

The belief that there is no significant difference between two variables or that the population parameter is greater than or equal to a specific value.

Logic of Hypothesis

The process of either rejecting or failing to reject a hypothesis based on the evidence.

Left Tailed Test

A hypothesis test where the population mean is less than a specific value.

Right Tailed Test

A hypothesis test where the population mean is greater than a specific value.

One-Tailed Test

A hypothesis test that is either left or right-tailed.

Two-Tailed Test

A hypothesis test that has two critical values and can either reject or fail to reject the null hypothesis.

T-test

A statistical test used to determine if there is a significant difference between the means of two groups.

Z-Score

A measure of how many standard deviations an observation or data point is from the mean.

R-Value

A statistical measure of the strength and direction of the linear relationship between two variables.

Outlier

A data point whose value is significantly greater than or less than the other values.

Cluster

An isolated group of points in a graph.

Gap

A large space between data points in a graph.

Histograms

A graph that uses rectangles to represent the frequency or relative frequency of each class.

Stem and Leaf Plots

A graphical representation of quantitative data where the stem represents the leftmost digits and the leaf represents the rightmost digit.

Box and Whisker Plots

A graph that shows the dispersion of data using quartiles and outliers.

Pareto Chart

A bar graph where the bars are drawn in decreasing order of frequency or relative frequency.

Pie Chart

A circle divided into sectors where each sector represents a category of data.

Dot Plot

A graph where each observation is represented by a dot placed above the observation.

Time Series Plot

A graph that shows the measurement of a variable over time.

Ogive

A graph that represents the cumulative or cumulative relative frequency of a class.

Degree of Confidence or Confidence Level

The level of certainty or probability associated with a confidence interval.

Margin of Error

The maximum likely difference between the true population parameter and a sample estimate of that parameter.

Population Proportion

The proportion or percentage of individuals in a population that exhibits a certain characteristic or attribute of interest.