A
al-Khwarizmi, Muhammad ibn Musa 116
genetic algorithms 126
alternating current 22
American Statistical Association 66
Arbuthnot, John 58
arithmetic mean 60
artificial intelligence (AI) 116, 130
artificial neural networks 126
Ashton, Kevin 128
autonomous vehicles 130
average
see mean
B
Bayesian networks 126
Bernoulli, Jacob 112
Bhaskara II 28
bias
numerical 102
big data 128
binomial distribution 36, 46, 51
Blackstone, Sir William 88
bootstrapping 72
Bowley, Sir Arthur Lyon 142, 146
Bradley, James 60
bus timetables 102
C
differential calculus 85
Cantor, Georg 26
Cardano, Gerolamo 22, 32, 52, 82
case-control studies 66
causal relationship 86
Central Limit Theorem 48
Chi-square distribution 36, 46, 56, 58
Chuprov, Alexander Ivanovich 40
cicadas 20
cluster sampling 42
Cochran, William Gemmell 64
combinations 120
common denominator 114
comparing numbers 138
complex conjugate 22
conditional probability 94
confidence interval 62, 70, 72
confidence level 88
conjugate 12
complex conjugate 22
continuous distributions 46
continuous numbers 26
continuous random variables 52
counting 108
D
data journalism 134
data-ink ratio 126
de Moivre, Abraham 48, 50, 82, 93
decimal point 110
decision tree 126
Dedekind, Richard 18
degrees of belief 90
del Ferro, Scipione 33
see also games of chance
differential calculus 85
dimensionality reduction 126
Diophantus of Alexandria 123
discrete distributions 46
discrete random variables 52
distance, measurement of 26
distribution
continuous 46
discrete 46
exponential 46
Gaussian 36
driverless cars 130
E
earthquakes 110
economic indicators 76
Efron, Bradley 72
Eratosthenes of Cyrene 20
Sieve of Eratosthenes 13
error
measurement error 64
random error 64
standard error 74
systematic error 64
ethical responsibility 86
irrational numbers 18
prime numbers 20
rational numbers 16
Euclidean algorithm 116
Euler, Leonhard 22
Euler’s identity 22
expert knowledge 82
exponential distribution 46
F
Fermat, Pierre de 80, 84, 94, 123
Fermat’s Little Theorem 80, 85
Fermat’s Principle of Least Time 80, 85
Fermat’s Two-square Theorem 80, 85
Fibonacci sequence 123
finance
commodity pricing 76
interest rates 112
negative numbers 28
stock prices 86
Fisher, Sir Ronald Aylmer 66
Frederick II 123
frequentist probability 82, 90
functions 44
Fundamental Theorem of Arithmetic 13, 20
G
Galois, Évariste 120
conditional probability 94
random variables 52
Gauss, Carl Friedrich 22, 36, 48
Gaussian distribution 36
genetic algorithms 126
geometric mean 60
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
index/indices 30
see also whole numbers
interest rates 112
internet identifiers 108
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
law enforcement
crime hotspots 86
presumption of innocence 88
racial profiling 86
testing laboratories 64
Leibniz, Gottfried Wilhelm 108
linear regression 76
logarithms 13, 22, 106, 106, 110
lotteries 120
M
machine learning 80, 86, 106, 116, 132
artificial neural networks 126
supervised 132
support vector machines 127
unsupervised 132
mammography screening 96
Marshall, Alfred 143
arithmetic 60
geometric 60
harmonic 60
standard error of the mean 74
measurement error 64
random 64
systematic 64
medicine
alcohol-related problems 98
bootstrapping 72
bowel cancer risk 100
false positives/negatives 118
immunization programme 88
Monty Hall problem 94
see also mean
N
n! 106
Napier, John 110
natural logarithm 22, 107, 110
Neyman-Pearson theory 69
Nightingale, Florence 38
normal distribution 46, 48, 51
null hypothesis 56, 58, 80, 88
null hypothesis significance test (NHST) 66
numerical bias 102
O
random 64
systematic 64
ordinary least squares 76
P
Pascal, Blaise 85
Pearson, Egon Sharpe 68
percentages 112
permutations 120
phi phenomenon 136
pi (π) 12
plausible values 56
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
conditional 94
subjective 80
probability distribution 46, 48
probability threshold 58
Q
R
racial profiling 86
radioactive decay 46
random error 64
random sampling 42
continuous 52
discrete 52
range rule 144
ranges 144
rectangular distribution
see uniform distribution
Richter scale 110
risk
Roman numerals 123
roots 30
S
samples 40
size 74
cluster 42
random 42
stratified 42
systematic 42
Samuel, Arthur Lee 132
scatter graph/plot 57, 76, 127, 140
Sieve of Eratosthenes 13
sigma (σ)
see standard deviation
sinusoidal wave 22
Spiegelhalter, David 98
square root (√) 12, 18, 30, 56
standard deviation 48, 51, 62, 72, 74, 144
standard error 74
standard error of the mean 74
statistical distribution 38, 46
statistical hypothesis 88
statistical independence 51
statistical inference
null hypothesis significance test 66
Chi-square distribution 36, 46, 56, 58
Student’s t-distribution 37, 46
Stein, Charles 102
Stifel, Michael 18
stock prices 86
stratified sampling 42
Student’s t-distribution 37, 46
subjective probability 80
support vector machines 127
systematic error 64
systematic sampling 42
T
t-distribution 37
Tartaglia, Niccolò 33
test statistic 88
testing laboratories 64
timetables 102
traffic flow 46
Tufte, Edward Rolf 134
Turing, Alan 130
U
V
visual communication theories (VCT) 134, 136
W
Weierstrass, Karl 18
Wertheimer, Max 136
see also integers
Wiles, Sir Andrew 85
Z