A-level Mathematics - Statistics Definitions (Edexcel)

Population

The whole set of items that are of interest

Census

Observes or measures every member of a population

Sample

Selection of observations taken from a subset of the population

Sampling unit

An individual item of a population

Sampling frame

A unique numbering or naming of sampling units to form a list

Simple random sample

Random sampling technique in which every member of the population has an equal chance of being selected

Systematic sampling

Random sampling technique in which elements are chosen at regular intervals from an ordered list

Stratified sampling

Random sampling technique in which the population is divided into mutually exclusive strata (classifications) and a random sample is chosen from each, maintaining the population's proportions lying within each strata

Quota sampling

Non-random sampling technique in which a sample is chosen by the researcher to represent the characteristics of the whole population

Opportunity (convenience) sampling

Non-random sampling technique in which elements are selected based on availability at the time of sampling, chosen to fit required criteria.

Quantitative data

Data associated with numerical observations

Qualitative data

Data associated with non-numerical observations

Continuous variable

A variable that can take any value in a given range

Discrete variable

A variable that can take only specific values in a given range

Classes

Groups in a grouped frequency table

Frequency polygon

The region formed by joining the middle of the top of each bar in a histogram

Bivariate data

Data which has pairs of values for two variables

Correlation

The nature of the linear relationship between two variables

Sample space

The set of all possible outcomes

Probability distribution

A full description of the probabilities of any outcome in the sample space

Test statistic

An observation or statistic calculated from a sample, used to test a hypothesis

Product moment correlation coefficient (PMCC)

A statistic describing the linear correlation between two variables. r represents the PMCC calculated from a given sample. ρ ("rho") is the population PMCC - always express a hypothesis in terms of ρ (r is the test statistic).

Actual significance level

The probability of incorrectly rejecting the null hypothesis (ie the chance that an observed result would fall in the critical region purely by chance if the model assumed by the null hypothesis were true).

Binomial model

Where there are a fixed number of trials; exactly two possible outcomes; a fixed probability of success at each trial and trials are independent of each other

Conditional probability

When the known occurrence of one event effects the probability of subsequent events.

Continuity correction

Adjusting the values of discrete variables to their upper and lower bounds when approximating with a continuous distribution such as the normal distribution

Critical region

A region of the probability distribution which, if the test statistic falls within it, leads to a rejection of the null hypothesis

Explanatory (independent) variable

This variable could be controlled by the researcher, and would usually be plotted on the x axis of a scatter graph

Extrapolation

Making a prediction based on a value outside the range of the given data

Hypothesis

A statement, which can be tested, about the value of a population parameter

Interpolation

Making a prediction for the dependent variable within the range of the given data set

Regression line

A straight line, expressed in the form y = a + bx , calculated to minimise the sum of the squares of the residuals

Linear interpolation

The method of approximating percentile or quartile frequencies within grouped data, assuming data is evenly distributed within each group.

Mutually exclusive

When events have no outcomes in common such that they cannot both occur at the same time.

Normal distribution

A continuous probability distribution, which is symmetrical about the mean. It forms a bell shaped curve with points of inflection one standard deviation above and below the mean

one-tailed / two-tailed test

A one-tailed test only has a critical region at one end of the distribution, whereas a two-tailed test has both extremes of the distribution included

Outlier

An extreme value lying outside the overall pattern of the data (usually identified from a given rule based on quartiles or standard deviations from the mean)

Parameter

A defining statistical characteristic of the population distribution

p-value

The probability of observing a tests statistic at or beyond the stated value, assuming the null hypothesis to be true

Response (dependent) variable

This variable is observed/ measured by the researcher and is usually plotted on the y axis of a scatter graph (and is represented by y in a regression equation)

Skewness

a non-symmetrical distribution, mostly commonly cited as evidence for the unsuitability of a normal model.

Standard error

The standard deviation of sample means, for samples of a given size, selected from a normal distribution

Statistically independent events

When the occurrence of one event does not effect another.

Uniform distribution

Where the probability is the same for each outcome

Hypothesis test

A statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population.