60 Fun Facts About Statistics

Which 18th-century German scholar gave the field its name, Statistik?

Gottfried Achenwall, a Göttingen professor, used the word Statistik in 1749 for the systematic description of a state's affairs, and the name stuck as the field turned mathematical.

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

The median is the middle value of sorted data; it resists distortion by a few huge values, which is why median income describes a typical household better than mean income.

What is the 'mode' of a data set?

The value that appears most often is the mode; a data set can have two modes (bimodal) or none at all if every value occurs just once.

Which Greek letter is conventionally used for standard deviation?

Sigma (σ) denotes the population standard deviation; a low sigma means data cluster tightly around the mean, while a high sigma means they are spread out.

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

68%: about 68% of values in a normal distribution lie within one standard deviation of the mean, and about 99.7% lie within three.

The normal distribution is also named after which mathematician?

Carl Friedrich Gauss gave the normal distribution its other name, the Gaussian, after using it in 1809 to model measurement errors in astronomy.

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

They tend toward a normal curve as samples grow: the central limit theorem says the distribution of sample means approaches normality whatever the population's shape, which is why normal-based methods work on non-normal data.

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

Large numbers law, better known as the law of large numbers, is why casinos win in the long run: over thousands of spins the average result settles at the expected value.

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

Guinness employed William Sealy Gosset at its Dublin brewery, where he devised the t-distribution to judge small samples of barley and stout; the firm made him publish under a pseudonym.

Under what pen name did William Sealy Gosset publish his t-distribution work?

Student was the pen name Gosset used for his 1908 paper 'The Probable Error of a Mean', which introduced the t-distribution for small samples.

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

Karl Pearson founded the Department of Applied Statistics at University College London in 1911, the world's first university statistics department, and also coined the term 'histogram'.

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

Ronald Fisher developed analysis of variance during his years at Rothamsted Experimental Station (1919-1933), where he analysed decades of crop-yield records.

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

P = 0.05, or 1 in 20, was the level called 'convenient' in the 1925 book Statistical Methods for Research Workers, and it became the default cut-off for significance.

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

The null hypothesis is what a p-value assumes: it gives the probability of data at least this extreme if the null were true, which the ASA's 2016 statement stressed is not the probability the hypothesis is true.

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

Francis Galton hit on regression through his 1875 sweet-pea breeding experiments and introduced the correlation coefficient in 1888, an idea later formalised by his protégé.

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

The next one is likely to be closer to average: an extreme score mixes skill with luck, and the luck rarely repeats, which is why the 'Sports Illustrated cover jinx' needs no curse.

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

Its effect: Bayes' theorem inverts conditional probability, turning the likelihood of an effect given a cause into the probability of the cause given its effect, updating a prior belief with evidence.

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

John Graunt, a London haberdasher, published Natural and Political Observations on the Bills of Mortality in 1662 and built the first crude life table from them.

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

Florence Nightingale drew her polar area diagrams in 1858 to show that disease, not wounds, killed most British soldiers in the Crimean War.

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

William Playfair, a Scottish engineer, had already introduced line and bar charts in his 1786 Commercial and Political Atlas before drawing the first pie charts in 1801.

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

John Tukey introduced the box-and-whisker plot in 1970 and popularised it in his 1977 book Exploratory Data Analysis; the box spans the middle half of the data.

What is the interquartile range?

The difference between the 75th and 25th percentiles is the interquartile range; because it ignores the tails, it is a robust measure of spread unaffected by outliers.

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

Standard deviations: a z-score is the value minus the mean, divided by the standard deviation, so z = 2 means two standard deviations above the mean.

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

Simpson's paradox: the classic example is UC Berkeley's 1973 graduate admissions, which looked biased against women overall but not within individual departments.

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?

Switch doors: switching wins the car two-thirds of the time, because the first pick is right only one time in three and the host's reveal moves the remaining odds to the other door.

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

Marilyn vos Savant answered the problem in her Parade 'Ask Marilyn' column in 1990; 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?

30%: Benford's law puts the leading digit 1 at about 30% of entries (log10 2 ≈ 0.301), a pattern Simon Newcomb spotted in worn logarithm tables in 1881.

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

The Literary Digest mailed ten million ballots drawn from its subscribers plus car and telephone lists, a sample skewed to the better-off, and folded within two years of the fiasco.

How large a sample did the American Institute of Public Opinion use for the 1936 election?

50,000: the American Institute of Public Opinion polled roughly 50,000 people chosen by quota sampling and correctly forecast Roosevelt's win, while a far larger mail-in poll got it wrong.

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

Survivorship bias: Wald reasoned the returning planes showed where hits could be survived, so armour belonged where they were undamaged, the places hits had downed the missing bombers.

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

They look completely different when graphed: Francis Anscombe built the four sets in 1973, each with the same means, variances, correlation and regression line, to show why you must plot your data.

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

Benjamin Disraeli was credited by Mark Twain in his autobiography, but the phrase appears nowhere in Disraeli's works and its true origin is unknown.

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

Deaths from horse kicks, tallied across Prussian cavalry corps over two decades, were shown by Ladislaus Bortkiewicz in 1898 to follow the Poisson distribution almost perfectly.

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

Adolphe Quetelet introduced his 'average man' in his 1835 book on social physics; Ancel Keys renamed the Quetelet Index the body mass index in 1972.

BMI is calculated by dividing weight in kilograms by what?

Height in metres squared: BMI = kg/m², so a 70 kg adult 1.75 m tall scores about 22.9; 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?

Nate Silver founded FiveThirtyEight in 2008 and called 49 of 50 states that year, then all 50 in 2012; his final 2016 forecast gave Trump roughly a 29% chance.

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

Gapminder, founded in 2005 by Hans Rosling with his son Ola and daughter-in-law Anna, built the Trendalyzer bubble charts he used in his TED talks, one of which ended with him swallowing a sword.

What is the first step in building a histogram?

Sorting values into bins comes first: a histogram divides the range into intervals (bins), counts the values in each, and draws bars whose heights show those counts.

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

The random sampling uncertainty is what a margin of error expresses: for a simple random sample of 1,000 people it is roughly ±3 percentage points at the usual confidence level.

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

95% is the conventional confidence level, corresponding to about 1.96 standard errors either side of the estimate, so roughly one interval in twenty misses the true value.

Which campaign does Charles Minard's celebrated 1869 flow map depict?

Napoleon's Russian campaign of 1812 is the subject of Minard's 1869 flow map, whose shrinking band shows the army falling from 422,000 men to 10,000.

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

Generalise from the sample to the population: random selection gives every member a known chance of inclusion, so the sample's results can be projected to the whole with a calculable margin of error.

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

r, the product-moment correlation coefficient, ranges from -1 (perfect negative) through 0 (no linear relation) to 1 (perfect positive).

What is a variable called when it drives both the supposed cause and the effect?

A confounding variable, like hot weather driving both ice-cream sales and drownings, influences both sides of an apparent relationship and can make a correlation masquerade as a cause.

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?

Sir John Sinclair borrowed the German term for his 21-volume Statistical Account of Scotland (1791-1799), a parish-by-parish survey compiled from questionnaires sent to every Church of Scotland minister.

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

The Trial of the Pyx, first recorded in 1282, tests a sample of newly struck coins for weight and purity; the pyx was the box that held the coins in Westminster Abbey's Pyx Chamber.

Which French mathematician first published the method of least squares, in 1805?

Adrien-Marie Legendre published the method of least squares in 1805 in a work on determining comet orbits, four years before a rival claimed to have used it earlier.

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

Abraham de Moivre derived the bell-shaped curve in 1733 as the limit of the binomial distribution for many coin tosses, in a note later folded into his Doctrine of Chances.

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

Ars Conjectandi, published in 1713 eight years after Jakob Bernoulli's death, contains his 'golden theorem' on long-run frequencies and introduced the Bernoulli numbers.

Which newly found body, lost in 1801, was relocated thanks to a young mathematician's orbit calculation?

Ceres, the first asteroid, was discovered by Giuseppe Piazzi on 1 January 1801 and lost in the Sun's glare; a 24-year-old German mathematician's orbit computation let astronomers find it again that December.

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

Richard Price, a Welsh minister and friend of Bayes, edited the essay and sent it to the Royal Society in 1763, two years after Bayes died.

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

1802: Laplace took the population-to-births ratio in a sample of départements and applied it to France's total annual births, an early ratio estimator, to reach 28,328,612.

Which statistician proposed the 'representative method' of sampling to the ISI in 1895?

Anders Nicolai Kiær, head of Norway's statistical bureau, urged the 'representative method' in 1895, surveying a cross-section instead of a full census; a 1934 paper later put random stratified sampling on a firm footing.

Which journal was founded in 1901 by Walter Weldon and two other pioneers of biometry?

Biometrika was founded in 1901 by Walter Weldon and two colleagues to publish statistical studies of biology; its first editor ran it until his death in 1936.

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

Egon Pearson and Jerzy Neyman laid out the framework of Type I and Type II errors and test power in papers from 1928 to 1933, with Neyman adding confidence intervals in the 1930s.

In which year was the term 'variance' introduced, in a paper on Mendelian inheritance?

1918: the paper 'The Correlation Between Relatives on the Supposition of Mendelian Inheritance' coined 'variance' and founded quantitative genetics by reconciling Mendel with biometric data.

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

Milk or tea poured first: Muriel Bristol claimed she could tell, so eight cups were prepared, four each way, and she was asked to sort them, a design described in The Design of Experiments (1935).

Which 1950s finding did the father of ANOVA publicly dispute, arguing correlation is not causation?

Smoking causes lung cancer was the finding he attacked in letters and a 1959 pamphlet, suggesting a common genetic cause; a pipe smoker, he also advised the tobacco industry.