60 Fun Facts About Statistics

The word 'statistics' comes from a German word originally meaning the description of what?

Statistik described the affairs of a state; today the field covers collecting, analysing and presenting any data.

Which measure of central tendency is the middle value when data are sorted?

It resists distortion by a few huge values, which is why median income beats mean income for describing a typical household.

What is the 'mode' of a data set?

In a perfect normal distribution the mode, median and mean all coincide.

Which Greek letter is conventionally used for standard deviation?

A low value means data cluster tightly around the mean; a high value means they are spread out.

In a normal distribution, roughly what percentage of values fall within one standard deviation?

The 68-95-99.7 rule extends the idea to two and three times the spread.

The normal distribution is also named after which mathematician?

Its symmetric shape earned the informal name 'bell curve', though other distributions are bell-shaped too.

What does the central limit theorem say about the spread of sample means?

That is why so many statistical methods built for normal data work on non-normal data.

Which law says the average of many independent samples converges to the true expected value?

It is why casinos win in the long run despite losing individual spins.

The t-distribution used for small samples was invented by a statistician working for which company?

William Sealy Gosset published as 'Student' because the brewery worried rivals would learn its secrets.

Under what pen name did brewer-statistician William Sealy Gosset publish?

His 1907 paper on counting cells with a haemocytometer independently rediscovered the Poisson distribution.

Who founded the world's first university statistics department, at University College London in 1911?

He also coined the term 'histogram' in his 1892 lectures and, less happily, championed eugenics.

Which statistician developed analysis of variance (ANOVA) while analysing crop data at Rothamsted?

He has been called the single most important figure in 20th-century statistics.

Which threshold did the man behind ANOVA popularise as 'convenient' for judging statistical significance?

He noted that P = 0.05, or 1 in 20, corresponds to about 1.96 standard deviations.

A p-value is the probability of results at least as extreme as those observed, assuming what is true?

The American Statistical Association warned in 2016 that p-values do not measure the probability that a hypothesis is true.

Who developed the statistical concept of correlation and promoted 'regression toward the mean'?

His sweet-pea experiments and 'bean machine' led him to the idea in the 1870s and 1880s.

What does 'regression toward the mean' predict about an extreme measurement?

It explains why the 'Sports Illustrated cover jinx' needs no curse.

Bayes' theorem lets you calculate the probability of a cause given what?

Bayes was a Presbyterian minister; Richard Price edited his essay and read it to the Royal Society in 1763.

Who is called the founder of demography for his 1660s study of London's mortality bills?

Graunt was a haberdasher by trade and produced the first life table.

Which nursing pioneer was also a statistical innovator, famous for her polar area (rose) diagrams?

Her charts showed that disease, not wounds, killed most soldiers in the Crimean War.

Who is credited with inventing the pie chart, in his 1801 Statistical Breviary?

The Scottish engineer had already introduced the line and bar chart in 1786, and may have been a British spy.

Who introduced the box-and-whisker plot in 1970?

The box shows the interquartile range; the whiskers reach out toward the extremes.

What is the interquartile range?

It ignores outliers, which makes it a robust measure of spread.

A z-score tells you how many of what a value lies above or below the mean?

Subtract the mean and divide by the standard deviation to get it.

Which name is given to a trend that appears in several groups but reverses when the groups are combined?

The classic example is UC Berkeley's 1973 graduate admissions, which looked biased against women overall but not by department.

How many people are needed in a room for a better-than-even chance that two share a birthday?

With 23 people there are 253 possible pairs, which is why the odds climb so fast.

In the Monty Hall problem, what should the contestant do after the host reveals a goat?

Switching wins the car two-thirds of the time; about 10,000 readers, nearly 1,000 with PhDs, wrote to tell the columnist she was wrong.

Which columnist's 1990 answer to the Monty Hall problem drew thousands of angry letters?

The puzzle had first been posed by Steve Selvin in The American Statistician in 1975.

According to Benford's law, about how often is 1 the leading digit in real-world numerical data?

Forensic accountants use it to sniff out faked figures; astronomer Simon Newcomb noticed it in worn logarithm tables in 1881.

Which magazine's 1936 poll of ten million people wrongly predicted Alf Landon would beat FDR?

It sampled its own readers plus car and telephone owners; George Gallup got it right with just 50,000 people.

How large a sample did the American Institute of Public Opinion use to call the 1936 election within 1.4%?

The lesson stuck: a representative sample beats a huge biased one.

Abraham Wald's WWII study of returning bombers is the classic example of correcting for which statistical error?

He estimated damage on the planes that never came back from the damage on those that did.

Anscombe's quartet is four data sets that share nearly identical summary statistics but differ how?

Francis Anscombe built them in 1973 to prove that you should always plot your data.

Twain popularised 'lies, damned lies, and statistics' by attributing it to which prime minister?

The phrase appears nowhere in Disraeli's works; its true origin is unknown.

The Poisson distribution was famously used in 1898 to model what in the Prussian army?

Ladislaus Bortkiewicz showed the rare events fit the distribution beautifully.

Which Belgian statistician devised the 'average man' concept and the index later renamed BMI?

Ancel Keys coined the term 'body mass index' for the Quetelet Index in 1972.

BMI is calculated by dividing weight in kilograms by what?

An adult BMI of 25 to 29.9 counts as overweight and 30 or more as obese.

Which statistician founded FiveThirtyEight and called 49 of 50 states correctly in the 2008 US election?

He gave Donald Trump a 28.6% chance in 2016, higher than most rival forecasts.

Swedish physician Hans Rosling co-founded which foundation to animate global development data?

He ended one TED talk by swallowing a sword, and his book Factfulness was published after his death.

What is the first step in building a histogram?

Karl Pearson coined the term in lectures at University College London in 1892.

What does a poll's 'margin of error' express?

The bigger it is, the less confident you should be that the poll matches a full census.

Which confidence level is used by default when none is stated?

It corresponds to about 1.96 standard errors either side of the estimate.

Which is a weakness experts most often cite about pie charts?

Research shows humans judge lengths far better than angles or areas.

Random sampling matters in statistics chiefly because it lets you do what?

When a full census is impossible, statisticians rely on carefully designed samples and experiments.

The product-moment correlation coefficient is abbreviated by which letter?

It ranges from -1 to 1 and was first developed with Auguste Bravais and Francis Galton in mind.

Which of these correctly describes the bias Abraham Wald corrected for?

Analysing only companies still in business makes past returns look rosier than they were.

Which company, founded in 1935 by the man who called the 1936 election, became famous for opinion polls?

George Gallup's institute made its name calling the 1936 election that humiliated a rival straw poll.

Who introduced the word 'statistics' into English in 1791 with his Statistical Account of Scotland?

The German Statistik, coined by Gottfried Achenwall in 1749, had meant the 'science of state'.

Which centuries-old test of the Royal Mint's coinage is an early example of statistical sampling?

A sample of coins from a box kept in Westminster Abbey has been tested for purity since the 12th century.

Who carried out the earliest known form of linear regression in 1700, analysing equinox data?

He wrote the first ordinary-least-squares normal equation while studying Hipparchus's observations.

Who first plotted the normal curve, in 1733, while studying coin tosses?

His curve came decades before Gauss, whose name is nonetheless attached to the distribution.

Which posthumous 1713 book by Jakob Bernoulli treated probability as a branch of mathematics?

It introduced the convention of writing certainty as one and probability as a number between zero and one.

Gauss famously used least squares in 1801 to predict the position of which body?

Legendre published the method first, in 1805; Gauss and Robert Adrain followed independently.

Who transmitted Thomas Bayes's proof to the Royal Society in 1763, after Bayes's death?

The word 'Bayesian' itself only appeared around 1950.

In what year did Laplace estimate France's population at 28,328,612 from births and sample towns?

He scaled up from three communities with 2,037,615 people and 71,866 births, an early ratio estimator.

Which Norwegian statistician introduced stratified sampling in 1895?

Neyman showed in 1934 that stratified random sampling generally beats purposive quota sampling.

Which journal did Karl Pearson found in 1901 with Walter Weldon and Francis Galton?

It was the first journal of mathematical statistics and biometry.

Which pair introduced the ideas of Type II error, test power and confidence intervals?

Neyman said the theory 'would look nicer' built without reference to Bayesian priors.

In which year did Fisher introduce the term 'variance' in a paper on Mendelian inheritance?

His additive genetic model from that paper is still used in genome-wide association studies.

Fisher's 'lady tasting tea' experiment tested her ability to detect what about her cup?

The thought experiment introduced his notion of a null hypothesis and uses Fisher's exact test.

Which 1950s finding did Fisher publicly dispute, arguing correlation does not imply causation?

A heavy pipe smoker and tobacco-industry consultant, he kept up the denial after retiring to Adelaide.