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What this book is
The ideas of statistics, explained slowly, from the very beginning. Which average to trust and when. What a standard deviation really measures. Where the bell curve comes from, and when not to use it. Why a poll of a thousand people can speak for millions, and what its margin of error leaves out. What a p-value is, in one sentence, and four things it isn’t. Why most alarms for rare things are false. How a correlation can mislead, and how a chart can fool you without a single false number.
It’s written for a student in a required statistics course, a new analyst, a manager handed a report, and anyone who reads the news. Every dataset is invented to make the method easy to see; every number in it was computed by program and checked a second way.
Every chapter, its worked examples, and its free calculator
The calculators are free, need no sign-up, and keep what you type in your own browser. Each one opens with the book’s own example loaded. The book is complete without them.
Part One · What You’ve Got
Calculators: Percentages
Worked examples 1–4
- Mina's order sheet: rows, columns and kinds of data
- A day's drinks: counts, shares and the mode
- Break-ins in two towns, per 1,000 homes
- Three questions to ask of a 4.6-star rating
Calculators: Mean, Median and Mode · Weighted Average
Worked examples 5–11
- A week of sales: the mean as fair share and balance point
- A founder walks into a bar: mean against median
- Six house prices and one mansion
- A shoe shop's best-selling size: the mode
- Ben's weighted course grade, and the final mark he needs
- Two classes of different sizes: the average of averages
- Eight waits: a long tail pulls the mean
Calculators: Describe Your Data
Worked examples 12–16
- Two cities, one average temperature: the range
- Ben's commute: quartiles and the middle half
- Five waits for a bus: a standard deviation by hand
- Two bakers' loaves: same mean, different spread
- Mice and elephants: relative spread
Calculators: Describe Your Data
Worked examples 17–22
- Sixty pizza deliveries in a histogram
- The same deliveries with three bin widths
- A box plot from five numbers
- The 1.5 × IQR fence: when is a delivery an outlier?
- Two rushes a day: the average customer arrives when nobody does
- Two branches' waits in side-by-side box plots
Calculators: Z-Score and Percentile
Worked examples 23–29
- Finishing 140th of 800: a percentile
- 85% on a quiz isn't the 85th percentile
- Ana's two exams compared by z-score
- Translating a standing from one exam to another
- A long jump against a sprint
- A negative z-score
- Can most drivers be better than average?
Part Two · Chance and the Bell Curve
Calculators: Expected Value · Dice Lab
Worked examples 30–36
- Six thousand rolls of a die: small samples wobble
- Two dice: why seven is most likely
- Rain and a late train: "and", "or" and "one minus none"
- "1 in 30" or "3%"? Natural frequencies
- A raffle ticket's expected value
- Five heads in a row, and how common streaks are
- The birthday surprise
Calculators: Bell Curve Areas
Worked examples 37–43
- Coin flips build a bell curve
- A milk steamer and the 68-95-99.7 rule
- A legal minimum fill: setting the machine
- Eggs between two weights
- Bolts outside their tolerance
- The score for the top 10%
- Pizza times are not a bell
Calculators: Dice Lab
Worked examples 44–48
- Averages of 1, 2, 5 and 25 dice: the central limit theorem
- Ten thousand coin flips: the law of large numbers
- Two maternity wards
- Why the best and worst schools are small
- The square-root law: four times the data for half the wobble
Part Three · From a Few to Everyone
Calculators: Random Sample Picker
Worked examples 49–54
- Oat milk and the 7am queue: a biased sample
- The 1936 Literary Digest poll
- Bomber damage and survivorship bias
- Star ratings: who writes reviews
- Two wordings, two answers
- A survey with a 20% response rate
Calculators: Margin of Error
Worked examples 55–60
- Where a poll's margin of error comes from
- Why population size hardly matters
- Sample size for a chosen margin
- Is a four-point lead real?
- The margin on a subgroup
- A hundred polls of a 50:50 town
Calculators: Confidence Interval
Worked examples 61–66
- Battery life: a confidence interval for an average
- Gosset's small samples and the t multiplier
- A hundred intervals: what "95% confident" means
- 90%, 95% and 99% intervals
- Two coffee blends: overlapping intervals
- How many waits to time
Part Four · Is It Real?
Calculators: Is It Just Luck?
Worked examples 67–71
- Fisher's eight cups of tea
- Sixty heads in a hundred flips
- One-sided and two-sided p-values
- A die that rolls too many sixes
- Two teaching methods: a shuffle test
Calculators: A/B Test
Worked examples 72–77
- An A/B test of a checkout button
- A thousand ideas: how many "significant" results are false
- A million visitors: significant but trivial
- Twenty customers: not significant, possibly big
- Twenty flavours: multiple comparisons
- Peeking at a test every day
Calculators: Base Rate and False Alarms · A/B Test (power)
Worked examples 78–83
- A "99% accurate" fraud alert
- A second, independent check
- A spam filter whose alarms can be trusted
- A smoke alarm's two settings: two kinds of error
- The power of a test
- The prosecutor's fallacy
Part Five · Two Things at Once
Calculators: Correlation and Best-Fit Line
Worked examples 84–89
- Temperature and iced drinks: a scatter plot and r
- A correlation by hand
- r²: how much temperature explains
- One odd point makes a correlation
- A strong curved pattern with r near zero
- Entrance tests and restricted range
Calculators: Correlation and Best-Fit Line
Worked examples 90–94
- Ice cream, sunburn and sunshine: a confounder
- Fire engines and damage: reverse causation
- Two rising trends, and their yearly changes
- Two delivery firms: Simpson's paradox
- A randomized garden trial
Calculators: Correlation and Best-Fit Line
Worked examples 95–100
- Taxi fares: slope and intercept
- Least squares you can see
- Predicting inside and outside the data
- A child's growth extrapolated to age 40
- Ordering ice from a regression line
- Two tests: regression to the mean
Part Six · Using It
Calculators: Chart Check
Worked examples 101–106
- A bar chart with a cut-off axis
- Pictures that grow in two directions
- "Doubles the risk": relative and absolute
- Percent or percentage points?
- Maps of counts against rates
- A cherry-picked starting point
Worked examples 107–107
- One survey headline, start to finish