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Quantitative Variables

Variables measured numerically

Categorical Variables

Variables representing categories

Nominal

Categorical variable with no order

Ordinal

Categorical variable with a clear order

Discrete Variable

Countable numerical variable

Continuous Variable

Variable that can take any value in an interval

Histogram

Graph showing frequency of data intervals

Bar Graph

Graph for categorical data with separated bars

Pie Chart

Graph showing proportions of categories

Stem-and-Leaf Plot

Displays data while preserving original values

Dot Plot

Each data point represented by a dot

Symmetric Distribution

Left and right sides are mirror images

Skewed Right

Tail extends to higher values

Skewed Left

Tail extends to lower values

Mean

Average of values

Median

Middle value of ordered data

Mode

Most frequent value

Range

Difference between max and min

Interquartile Range (IQR)

Q3 - Q1

Variance

Average squared deviation from mean

Standard Deviation

Square root of variance

Five-Number Summary

Min, Q1, Median, Q3, Max

Boxplot

Graph of five-number summary

1.5×IQR Rule

Method to detect outliers

Population

Entire group of interest

Sample

Subset of population

Parameter

Numerical summary of population

Statistic

Numerical summary of sample

Census

Data collection from entire population

Random Sampling

Each individual has equal chance

Bias

Systematic error in data collection

Probability

Measure of likelihood of an event

Experiment

Procedure producing outcomes

Event

Outcome or set of outcomes

Sample Space

Set of all possible outcomes

Complement

All outcomes not in the event

Union

All outcomes in either event

Intersection

Outcomes in both events

Mutually Exclusive

Events cannot occur together

Independent Events

One event does not affect the other

Conditional Probability

Probability of A given B

Random Variable

Variable taking numerical values based on chance

Discrete Random Variable

Variable with countable values

Continuous Random Variable

Variable with any value in interval

Probability Distribution

Probabilities of all possible values

Expected Value

Mean of a random variable

Standard Deviation of Random Variable

Square root of variance

Binomial Distribution

Counts successes in n trials

Mean of Binomial

n*p

Variance of Binomial

np(1-p)

Normal Distribution

Symmetric, bell-shaped distribution

Z-Score

Number of standard deviations from mean

Empirical Rule

68% within 1 SD, 95% within 2 SDs

Central Limit Theorem

Sample means ~ normal if n large

Sampling Distribution

Probability distribution of a sample statistic

Standard Error

SD of a sampling distribution

Confidence Interval

Range of plausible values for a parameter

Margin of Error

Max expected difference between statistic and parameter

Level of Confidence

Probability interval contains true parameter

Hypothesis Testing

Procedure to test a claim about a population

Null Hypothesis (H0)

Assumes no effect or difference

Alternative Hypothesis (Ha)

Claim being tested

Significance Level (α)

Threshold for rejecting H0

p-Value

Probability of observing data assuming H0 true

Type I Error

Reject H0 when it is true

Type II Error

Fail to reject H0 when it is false

One-Tailed Test

Hypothesis test in one direction

Two-Tailed Test

Hypothesis test in both directions

t-Test

Hypothesis test for small samples

Correlation

Measures strength and direction of linear relationship

Regression

Predicts one variable using another

Slope (b)

Change in y per unit change in x

Intercept (a)

Value of y when x = 0

Residual

Difference between observed and predicted value

Coefficient of Determination (R²)

Proportion of variation in y explained by x

Outlier

Data point far from others

Influential Point

Data point strongly affecting regression line