Statistics key terms

The variable whose response is being investigated, plotted on the vertical y-axis; also called the response variable.

Numerical data that take separate, distinct values, such as the number of books borrowed.

The spread or variability of the values in a data set.

The pattern of values in a dataset, including where they are centred and how widely they are spread.

The coordinate $(\bar{x},\bar{y})$, found by calculating the mean of the x-values and the mean of the y-values separately.

The approximate normal-distribution rule that 68% of values lie within one standard deviation of the mean, 95% lie within two, and values more than three standard deviations away are very unusual.

An approximate value for an unknown population characteristic, obtained using available data.

A concern about whether an investigation treats participants fairly and protects their well-being, privacy and voluntary choice to take part.

A critical review of a statistical investigation that identifies weaknesses, considers their effects and suggests improvements.

An event is equally likely to happen as not to happen; its probability is $\frac{1}{2}=0.5=50\%$. Also called ‘evens’.

A set of outcomes of a probability experiment, such as rolling an even number on a die.

A set of events that together includes every possible outcome. At least one of the events must occur.

The predicted number of occurrences of an event, calculated by multiplying its probability by the number of trials.

The long-run average value of a random variable over many repetitions. For $X\sim B(n,p)$, the expected value is $np$.

An estimate of probability calculated as $\frac{\text{frequency of the event}}{\text{total number of trials}}$; also called relative frequency.

The variable whose changes are used to investigate or explain changes in another variable. Also called the independent variable.

A character or notation that is not needed in the values being processed, such as a unit label attached to each number in a spreadsheet column.

A variable other than the explanatory variable being investigated that could affect the response variable.

Using an existing trend to estimate a value beyond the time range of the observed data.

Any outcome that is not a success. If the probability of success is $p$, the probability of failure is $1-p$.

A die for which each face has an equal probability of landing uppermost.

An experiment conducted in the subjects' usual environment, with the researcher controlling some conditions or variables.

The number of times a value or category occurs in a data set.

The frequency per unit of class width: $\text{frequency density}=\frac{\text{frequency}}{\text{class width}}$.

A graph formed by plotting class frequencies at class midpoints and joining successive points with straight lines.

A table showing the number of observations in each value or category.

The underlying direction of change in a time series, shown by a trend line rather than its repeated short-term fluctuations.

A genuine observation that is unusually large or small compared with the rest of the data.

For positive numerical values, an average found by multiplying the values together and taking the root corresponding to the number of values: $G=(x_1x_2\cdots x_n)^{1/n}$.

The change in the vertical-axis quantity divided by the corresponding change in the horizontal-axis quantity: $m=\frac{y_2-y_1}{x_2-x_1}$.