Maths AI terms: B

B

Back bearingalso reverse bearing, return bearing, back bearings

The bearing of the starting point from the destination, which differs from the original bearing by 180°.

Introduced in 3.3 Applications of trigonometry

Basealso base of a power, base of a logarithm

The number that is multiplied by itself in a power, written $a$ in $a^n$; in a logarithm $\log_a b$, the base $a$ is the number that is raised to a power.

Introduced in 1.5 Exponents and introduction to logarithms

Base vectorsHL only · also base vector, standard basis vectors, ijk notation, i, j, k

The vectors $\boldsymbol{i}$, $\boldsymbol{j}$ and $\boldsymbol{k}$ of length 1 in the positive directions of the $x$-, $y$- and $z$

Bearingalso three-figure bearing, bearings, compass bearing, true bearing

The direction of one point from another, given as the angle measured clockwise from north, written with three digits from 000° to 360°.

Introduced in 3.3 Applications of trigonometry

Bernoulli trialalso Bernoulli trials, Bernoulli experiment

A random trial with exactly two possible outcomes, called success and failure, where success has a fixed probability $p$.

Introduced in 4.8 The binomial distribution

Biasalso sampling bias, biased sample, biased, non-response bias, selection bias

A systematic tendency for a sample, or for the way data are collected, to give results that differ from the true population values in a particular direction.

Introduced in 4.1 Collecting data and sampling

Biased estimatorHL only · also biased estimate, bias of an estimator

An estimator whose expected value differs from the population parameter it estimates, so that it tends to overestimate or to underestimate.

Introduced in 4.14 Linear transformations of random variables

Biased questionHL only · also leading question, unbiased question, biased questions, leading questions

A question whose wording, order or answer options encourage a particular response, so that the answers do not reflect respondents' true views; a question free of this is an unbiased question.

Introduced in 4.12 Data collection and reliability

Bibliographyalso bibliographies, reference list, works cited, references

The full list of sources used in a piece of work, placed at the end and given in one consistent referencing style, with enough detail for a reader to find each source.

Binomial coefficientalso nCr, n choose r, binomial coefficients

The number of ways to choose $r$ items from $n$ when order does not matter, written $\binom{n}{r}$ or ${}^{n}C_{r}$

Binomial distributionalso B(n, p), binomial random variable, X ~ B(n, p), binomial model, binomially distributed

The probability distribution of the number of successes $X$ in a fixed number $n$ of independent trials, each with the same probability of success $p$; it is written $X \sim \mathrm{B}(n, p)$.

Introduced in 4.8 The binomial distribution

Binomial testHL only · also test for a proportion, binomial hypothesis test, binomial tests

A hypothesis test for a population proportion $p$, in which the number of successes in $n$ independent trials is modelled by $\mathrm{B}(n, p_0)$ when the null hypothesis $p = p_0$

Bisectoralso bisect, bisects, bisecting, bisectors

A line, ray or segment that divides a line segment or an angle into two equal parts.

Introduced in 3.5 Perpendicular bisectors

Bivariate dataalso bivariate, paired data, bivariate data set

Data in which two variables are measured or observed for each individual, so that each individual gives an ordered pair of values $(x, y)$.

Introduced in 4.4 Correlation and regression

Bivariate normal distributionHL only · also bivariate normal, bivariate normally distributed

A joint distribution of two random variables in which each variable is normally distributed and, for any value of one, the other is normally distributed with a mean that depends linearly on it.

Introduced in 4.18 Further hypothesis testing

Boundary conditionalso boundary conditions, initial condition, initial conditions

A known pair of corresponding values of the variables, used to find the constant of integration and so select one function from the family of anti-derivatives.

Introduced in 5.5 Introduction to integration

Box-and-whisker diagramalso box plot, box plots, box-and-whisker plot, box and whisker diagram, box-and-whisker diagrams

A diagram drawn against a scale in which a box spans the lower to the upper quartile with a line at the median, and whiskers extend from the box to the smallest and largest values that are not outliers; any outliers are marked separately with a cross.

Introduced in 4.2 Presenting data

Break-even pointalso break-even, break even, break-even points, break-even quantity

A level of output at which total revenue equals total cost, so the profit is zero; graphically, a point of intersection of the revenue and cost graphs.

Introduced in 2.4 Key features of graphs