Topic
Data
Numbers describing the world. Collect them, draw them, average them, reason about the chance behind them — the math of evidence.
From counts to conclusions
Data work has a natural arc. Collect some numbers, draw them so you can see the shape, summarise the centre and the spread, then reason about probability and inference — what the sample tells you about the population behind it. The sections below walk that arc.
Collecting & describing data
Where data comes from — what to ask, who to ask, and how to record it.
Discrete vs continuous
Counts vs measures — the two flavours of data.
Univariate vs bivariate
One variable or two — different questions, different tools.
Surveys
Design good questions, gather honest answers, analyse the results.
Sampling
Pick a small group to learn about a big one — without bias.
Tally marks
The fastest way to count by hand — strokes in groups of five.
Charts & graphs
Pictures of data — bar, line, pie, histogram, dot, stem-and-leaf — and how to spot the ones that lie.
Charts
Bar, pie, line — the same numbers told three ways.
Bar graphs
Compare categories at a glance — taller bar means bigger.
Pictographs
Pictures stand in for counts — friendly charts for small data.
Line graphs
Connect points to track change over time.
Pie charts
Slices of a circle — each one a percentage of the whole.
Histograms
Bar charts for grouped numerical data — bins on the x-axis.
Dot plots
One dot per data point — see exactly where each value lands.
Stem & leaf plots
An old-school way to see distribution without losing the actual numbers.
Box & whisker plots
Five-number summaries you can compare at a glance.
Misleading graphs
Truncated axes, 3D pies, cherry-picked ranges — how charts lie.
Central value (averages)
Mean, median, mode — three answers to 'what's a typical value?'
Averages
Mean, median, mode, range — interactive.
Mean
Add them all, divide by how many — the everyday average.
Median
The middle value when sorted — robust against outliers.
Mode
The value that appears most often.
Weighted mean
Some data points count more — multiply, then divide by total weight.
Spread & distribution
Not just the middle — how tightly or loosely the data clusters around it.
Range
Largest minus smallest — the simplest spread.
Spread & quartiles
Range, IQR, standard deviation — how spread out is the data?
Mean deviation
On average, how far is each value from the mean?
Standard deviation
The typical distance of a value from the mean — spread, summarised.
Quartiles
Split sorted data into four equal groups — Q1, Q2 (median), Q3.
Percentiles
The 90th percentile means 90% of values fall below — used for ranks.
Outliers
Data points way outside the pack — notice them, investigate, decide.
Frequency distribution
How often each value (or range) appears — turn a list into a table.
Cumulative frequency
Running total — and the curve it builds.
Two variables — coordinates & correlation
When each data point is a pair (x, y) — plot it, fit a line, ask if x predicts y.
Cartesian coordinates
(x, y) — the original way to put numbers on a plane.
Scatter plots
Two variables, one dot per data point — patterns appear.
Correlation
Do tall people weigh more? Plot the scatter and read the trend.
Least-squares regression
Find the line that minimises total squared error — the line of best fit.
Probability basics
Chance, events, and how to combine them — multiply, add, complement.
Probability
Roll dice and flip coins as many times as you like.
Independent events
One coin flip doesn't affect the next — multiply their probabilities.
Mutually exclusive events
Can't both happen at once — add their probabilities.
Complement
P(not A) = 1 − P(A). The 'everything else' rule.
Conditional probability
P(A given B) — once you know B happened, A's chances change.
Probability tree diagrams
Branch out the possibilities — multiply along, add across.
Counting principle
If A has m ways and B has n ways, the pair has m·n ways.
Combinations & permutations
Pick 3 from 10 — does order matter? Choose your formula.
Distributions
The shapes that data takes — normal bell curves, binomial counts, skewed tails.
Random variables
A variable whose value is the outcome of a random event.
Normal distribution
The bell curve — why so much of the world clusters around an average.
Standard normal
Mean 0, SD 1 — the bell curve everyone calibrates against.
Binomial distribution
n trials, each with p chance of success — count the wins.
Skewness
How lopsided is the distribution? Tail to the left or right.
Inference & advanced
From a sample to a conclusion — confidence intervals, hypothesis tests, classic paradoxes.
Confidence intervals
Wrap a margin of error around an estimate — and quantify your trust.
Student's t-test
Compare means with small samples — the workhorse of stats.
Chi-square test
Test whether observed counts match what you expected.
Bayes' theorem
Update your beliefs when new evidence shows up.
Birthday paradox
Just 23 people — and there's a 50% chance two share a birthday.
Quincunx (Galton board)
Drop balls through pegs — watch the bell curve build itself.