Statistics Concepts
Explore K-12 statistics concepts with instant definitions, formulas, examples, and connected explanations. Learn how data displays, probability, sampling, and inference fit together.
Explore by Topic
Data Collection & Displays
Statistical questions, tables, graphs, and choosing the right display
16 conceptsCenter, Spread & Distributions
Mean, median, variability, quartiles, outliers, and distribution shape
19 conceptsProbability & Chance
Sample spaces, compound events, tree diagrams, and conditional probability
13 conceptsSampling, Design & Inference
Sampling, bias, experiments, confidence intervals, and hypothesis tests
19 conceptsRelationships & Regression
Scatter plots, correlation, two-way tables, residuals, and regression
11 conceptsBrowse by Grade Band
Statistics begins with sorting and graphs, then grows into probability, sampling, regression, and inference.
Sorting objects, noticing categories, and talking about simple class data.
Picture graphs, line plots, basic probability language, and early averages.
Dot plots, histograms, mean, median, variability, and random sampling.
Conditional probability, inference, regression, experiments, and significance.
Popular Concepts
Mean as Fair Share
The mean (average) represents what each person would get if the total were divided equally among everyone. It is calculated by adding all values and dividing by the count, giving a single number that summarizes the center of the data.
Median
The median is the middle value when all data points are arranged in order from smallest to largest. Half the values lie above it and half below. For an even number of values, the median is the average of the two middle values.
Basic Probability
Probability is the measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). It is calculated as the ratio of favorable outcomes to total possible outcomes when all outcomes are equally likely.
Conditional Probability
Conditional probability is the probability that one event happens given that another event has already happened. It narrows the sample space to the cases where the given condition is true.
Standard Deviation
Standard deviation is a measure of how spread out data values are from the mean, representing the typical distance of data points from the average. A small standard deviation means data clusters tightly around the mean; a large one means data is widely spread.
Confidence Interval
A confidence interval is a range of values, calculated from sample data, constructed so that the procedure captures the true population parameter a specified percentage of the time (e.g., 95%). It quantifies the uncertainty inherent in using a sample to estimate a population value.
Line of Best Fit
The line of best fit (trend line) is the straight line that best represents the overall trend in a scatter plot by minimizing the sum of squared vertical distances between the line and all data points. Its equation enables predictions for new x-values.
Linear Regression
Linear regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a straight line that minimizes the sum of squared distances from data points to the line (least squares method).
Hypothesis Testing
Hypothesis testing is a formal statistical procedure for using sample data to decide between two competing claims about a population parameter. You state a null hypothesis (no effect) and an alternative hypothesis, collect data, compute a test statistic, and determine whether the evidence is strong enough to reject the null.
Sampling Variability
Sampling variability is the natural sample-to-sample difference that appears when we take repeated random samples from the same population. Even good random samples do not all produce identical statistics.
Histogram
A histogram is a graph that groups numerical data into equal-width ranges (bins) and shows the frequency of values in each range using adjacent bars that touch. Unlike bar graphs, histograms display the distribution shape of continuous data.
Sampling Bias
Sampling bias occurs when a sample is collected in a way that systematically makes some members of the population more likely to be included than others, producing results that do not accurately represent the full population and leading to misleading conclusions.
Statistics Guides
Priority guides and concept pages that go beyond short definitions with formulas, examples, FAQs, common mistakes, and stronger statistics-to-statistics links.
Statistics for Students
A broad student-friendly guide to graphs, averages, probability, spread, and reading data honestly.
Data Representation, Variability, and Sampling
Displays, sample spaces, sampling distributions, residuals, and stronger links across core statistics ideas.
Mean
Definition, formula, when to use it, worked examples, FAQs, and related center measures.
Conditional Probability
How the sample space changes, how to use two-way tables, and where students usually get stuck.
Confidence Interval
Estimate population values with margin of error, standard error, and interpretation guidance.
Linear Regression
From scatter plots to fitted models, residuals, and prediction limits.
Features
Clear First Explanations
Every statistics page starts with a direct definition before symbols, formulas, or formal interpretation.
Formula With Context
Formula sections explain when a rule applies, what each quantity means, and when the calculation would overclaim.
Connected Statistics Links
Statistics pages now link more strongly across displays, probability, sampling, regression, and inference.
Use the full statistics cluster
Move between concepts, comparison pages, and common-mistake pages when a dataset feels clear numerically but shaky conceptually.