maths statistics definitions

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

Conditional probability

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

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

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.

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

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