INDEX

A

absolute risk 98, 100

al-Khwarizmi, Muhammad ibn Musa 116

algorithmic bias 126, 130

algorithms 80, 86, 116, 126

genetic algorithms 126

learning algorithms 127, 132

alternating current 22

alternative hypothesis 58, 88

American Statistical Association 66

ANOVA test 56, 58

Arbuthnot, John 58

arithmetic mean 60

artificial intelligence (AI) 116, 130

artificial neural networks 126

Ashton, Kevin 128

autonomous vehicles 130

average

see mean

Avogadro’s number 12, 14

B

base 106, 108

Bayes’ Theorem 90, 93

Bayes, Thomas 90, 92

Bayesian networks 126

Bayesian probability 82, 90

bell curve 36, 48

Bernoulli, Jacob 112

Bhaskara II 28

bias

algorithmic 126, 130

numerical 102

big data 128

binary 106, 108

binary digits (bits) 12, 24

binary number 24, 108

binomial distribution 36, 46, 51

Blackstone, Sir William 88

bootstrapping 72

Bowley, Sir Arthur Lyon 142, 146

Bradley, James 60

bus timetables 102

C

calculus 28, 85, 110

differential calculus 85

cancer 96, 100

Cantor, Georg 26

Cardano, Gerolamo 22, 32, 52, 82

case-control studies 66

causal relationship 86

census 36, 40

Central Limit Theorem 48

Chi-square distribution 36, 46, 56, 58

Chuprov, Alexander Ivanovich 40

cicadas 20

cluster sampling 42

clusters 36, 42, 132

Cochran, William Gemmell 64

coin tossing 52, 82, 90

colour 134, 136

combinations 120

common denominator 114

comparing numbers 138

complex conjugate 22

complex numbers 22, 48, 51

composite number 12, 20

conditional probability 94

confidence interval 62, 70, 72

confidence level 88

conjugate 12

complex conjugate 22

constants 14, 51

continuous distributions 46

continuous numbers 26

continuous random variables 52

correlation 76, 140

counting 108

critical value 80, 88

cryptography 12, 20

D

data journalism 134

data visualization 126, 134

data-ink ratio 126

de Moivre, Abraham 48, 50, 82, 93

de Moivre’s formula 48, 51

decimal point 110

decimals 26, 112

decision tree 126

Dedekind, Richard 18

deep learning 126, 130

degrees of belief 90

del Ferro, Scipione 33

denominator 12, 106, 114

dependent variables 44, 76

Descartes, René 14, 22

diagnostic testing 96, 118

dice 33, 52, 94

see also games of chance

differential calculus 85

dimensionality reduction 126

Diophantus of Alexandria 123

discrete distributions 46

discrete numbers 20, 24, 52

discrete random variables 52

distance, measurement of 26

distribution

binomial 36, 46, 51

Chi-square 36, 46, 56, 58

continuous 46

discrete 46

exponential 46

Gaussian 36

normal 46, 48, 51

Poisson 36, 46

probability 46, 48

statistical 38, 46

uniform 37, 46

driverless cars 130

E

e 22, 106, 110

earthquakes 110

economic indicators 76

Efron, Bradley 72

encryption 12, 20

enumerators 36, 40

Eratosthenes of Cyrene 20

Sieve of Eratosthenes 13

error

measurement error 64

observation error 56, 64

random error 64

standard error 74

systematic error 64

type I errors 88, 118

type II errors 88, 118

ethical responsibility 86

Euclid 12, 16

irrational numbers 18

prime numbers 20

rational numbers 16

Euclidean algorithm 116

Euler, Leonhard 22

Euler’s identity 22

expert evidence 82, 93

expert knowledge 82

exponential distribution 46

exponential function 12, 22

exponents 13, 30

F

false negatives 80, 118

false positives 80, 118

Fermat, Pierre de 80, 84, 94, 123

Fermat’s Last Theorem 80, 85

Fermat’s Little Theorem 80, 85

Fermat’s Principle of Least Time 80, 85

Fermat’s Two-square Theorem 80, 85

Fibonacci 114, 122

Fibonacci sequence 123

finance

commodity pricing 76

interest rates 112

investment decisions 62, 93

negative numbers 28

stock prices 86

Fisher, Sir Ronald Aylmer 66

forensic science 82, 93

fractions 16, 112, 114

Frederick II 123

frequentist probability 82, 90

functions 44

Fundamental Theorem of Arithmetic 13, 20

G

Galois, Évariste 120

games of chance 33, 48, 51

conditional probability 94

dice 33, 52, 94

random variables 52

Gauss, Carl Friedrich 22, 36, 48

Gaussian distribution 36

genetic algorithms 126

geometric mean 60

Gestalt laws 126, 136

golden ratio 123

googol 30

Gosset, William Sealy 37

graphs 38

Bayesian networks 126

scatter graph/plot 56, 76, 127, 140

Graunt, John 86

greatest common divisor (GCD) 106, 116

H

harmonic mean 60

health see medicine

Heron of Alexandria 22

Hindu-Arabic numerals 123

Hippasus of Metapontum 18

hiring practices 130

Hume, David 93

hypothesis testing 38, 46, 70, 88

Neyman-Pearson theory 69

null hypothesis significance test 66

I

imaginary number (i) 13, 22, 33

immunization programme 88

independent variables 44, 76

index/indices 30

inferential statistics 36, 46

integers 13, 14, 24, 106, 107

see also whole numbers

interest rates 112

internet identifiers 108

Internet of Things 127, 128

IQ 46

irrational numbers 14, 16, 18, 106, 110

pi (π) 12

K

Kahneman, Daniel 118

Koffka, Kurt 136

Köhler, Wolfgang 136

Kolmogorov, Andrey 44

L

Laplace, Pierre-Simon 42, 48

law enforcement

crime hotspots 86

expert evidence 82, 93

forensic science 82, 93

presumption of innocence 88

racial profiling 86

testing laboratories 64

learning algorithms 127, 132

Leibniz, Gottfried Wilhelm 108

likelihood ratio 69, 82, 96

linear regression 76

logarithms 13, 22, 106, 106, 110

lotteries 120

M

machine learning 80, 86, 106, 116, 132

algorithms 127, 132

artificial neural networks 126

supervised 132

support vector machines 127

unsupervised 132

mammography screening 96

Marshall, Alfred 143

mean 48, 58, 60, 62, 138

arithmetic 60

geometric 60

harmonic 60

mu (μ) 36, 48

population mean 60, 74

sample mean 60, 74

standard error of the mean 74

measurement error 64

random 64

systematic 64

median 56, 60

medicine

alcohol-related problems 98

bootstrapping 72

bowel cancer risk 100

decision-making 76, 98, 100

diagnostic testing 96, 118

false positives/negatives 118

immunization programme 88

mode 56, 60

Monty Hall problem 94

mu (μ) 36, 48

see also mean

N

n! 106

Napier, John 110

natural logarithm 22, 107, 110

natural numbers 13, 14

negative numbers 22, 28, 33

Newton, Isaac 51, 85

Neyman, Jerzy 69, 70

Neyman-Pearson theory 69

Nightingale, Florence 38

normal distribution 46, 48, 51

null hypothesis 56, 58, 80, 88

null hypothesis significance test (NHST) 66

numerator 13, 107, 114

numerical base 106, 108

numerical bias 102

O

objective probability 80, 82

observation error 56, 64

random 64

systematic 64

ordinary least squares 76

P

p-values 57, 58, 66

Pascal, Blaise 85

Pearson, Egon Sharpe 68

Pearson, Karl 69, 76

percentages 112

permutations 120

petabyte (PB) 80, 86

phi phenomenon 136

pi (π) 12

place-value 107, 108, 123

plausible values 56

point estimate 57, 70

Poisson distribution 36, 46

polynomials 13, 14, 22, 120

population 36, 38, 40

subpopulation 37, 40

population census 36, 40

population mean 60, 74

positive integers 24

powers 30

prediction 86

presumption of innocence 88

Priestley, Joseph 144

prime numbers 20

Fundamental Theorem of Arithmetic 12, 20

Sieve of Eratosthenes 13

principle of least action 85

prior degree of belief 90, 93

probability 33, 70, 82

Bayesian 82, 90

conditional 94

frequentist 82, 90

objective 80, 82

subjective 80

probability distribution 46, 48

probability threshold 58

Q

quality control 42, 69

quartiles 144, 146

R

racial profiling 86

radioactive decay 46

random error 64

random sample 46, 48

random sampling 42

random variables 46, 52

continuous 52

discrete 52

range rule 144

ranges 144

rational numbers 14, 16

real numbers 14, 26

rectangular distribution

see uniform distribution

relative risk 98, 100

reproducibility crisis 57, 66

Richter scale 110

risk

absolute 98, 100

relative 98, 100

Roman numerals 123

roots 30

S

sample mean 60, 74

samples 40

random 46, 48

size 74

sampling 42, 143

cluster 42

random 42

stratified 42

systematic 42

Samuel, Arthur Lee 132

scatter graph/plot 57, 76, 127, 140

shape and colour 134, 136

Sieve of Eratosthenes 13

sigma (σ)

see standard deviation

significance level 57, 58

sinusoidal wave 22

smokers 44, 72

Spiegelhalter, David 98

square root (√) 12, 18, 30, 56

negative numbers 22, 33

standard deviation 48, 51, 62, 72, 74, 144

sigma (σ) 36, 48, 56, 126

standard error 74

standard error of the mean 74

statistical distribution 38, 46

statistical hypothesis 88

statistical independence 51

statistical inference

likelihood ratio 69, 82, 96

null hypothesis significance test 66

statistical tests 38, 58

ANOVA 56, 58

Chi-square distribution 36, 46, 56, 58

p-values 58, 66

significance level 57, 58

Student’s t-distribution 37, 46

t-test 57, 58

statistics 33, 38

inferential 36, 46

Stein, Charles 102

Stifel, Michael 18

stock prices 86

strata 37, 42

stratified sampling 42

student grades 144, 146

Student’s t-distribution 37, 46

subjective probability 80

subpopulation 37, 40

support vector machines 127

systematic error 64

systematic sampling 42

T

t-distribution 37

t-test 57, 58

Tartaglia, Niccolò 33

temperature 64, 66

test statistic 88

testing laboratories 64

timetables 102

tossing a coin 52, 82, 90

traffic flow 46

trends 38, 86, 128, 140

Tufte, Edward Rolf 134

Turing, Alan 130

type I errors 88, 118

type II errors 88, 118

U

uncertainty 64, 74, 138

uniform distribution 37, 46

V

variables 44, 58

dependent 44, 76

independent 44, 76

random 46, 52

variance 48, 57, 62, 144

visual communication theories (VCT) 134, 136

W

weather 44, 116

Weierstrass, Karl 18

Wertheimer, Max 136

whole numbers 16, 18, 24, 107

see also integers

Wiles, Sir Andrew 85

Z

zero 16, 28