GCSE Statistics key terms

The whole group of people or items that a study is about, for example every student in a school. Data is collected from it, or from part of it, to answer a question.

A smaller group chosen from a population and used to stand in for it. Data from the sample is used to draw conclusions about the whole population when surveying everyone would be too costly or slow.

A survey that collects data from every single member of a population. It gives the most complete picture but is expensive and slow, and can be impractical for large groups.

A list of all the individuals or items in a population from which a sample is chosen, such as a register of names. If the list is incomplete or out of date, the sample may be biased.

A method where every member of the population has an equal chance of being chosen and each pick is independent, for example drawing names from a hat or using random numbers.

A method that picks members at regular intervals from an ordered list, such as every tenth name, after a random starting point. It is quick, but a repeating pattern in the list can make it biased.

The population is split into groups that share a characteristic, and a sample is taken from each group in proportion to its size, so the sample mirrors the structure of the population.

An interviewer fills set numbers for particular groups, such as age or sex, by choosing anyone available until each quota is met. It is quick but not random, so results can be biased.

A flaw in how a sample is chosen or how data is collected that makes results differ from the truth in a consistent direction, usually by over-representing some parts of the population.

Data that can only take particular separate values, usually whole numbers obtained by counting, such as the number of siblings a student has. Values in between are not possible.

Data that can take any value within a range and is measured rather than counted, such as height or time. The recorded value depends on how precisely the measurement is made.

A range of values used to group data in a frequency table, such as 10 to under 20. Intervals should not overlap and are usually the same width so the data can be compared fairly.

The frequency of a class divided by its width. It is plotted on the vertical axis of a histogram so that the area of each bar, rather than its height, represents the frequency.

A chart for continuous grouped data in which the bars touch. The area of each bar shows the frequency, so classes of unequal width are handled correctly by plotting frequency density.

A running total of frequencies up to a given value. Plotting cumulative frequency against the upper class boundaries gives a curve from which the median and quartiles can be read.

The total of all the values divided by how many values there are. It uses every piece of data, but one very large or very small value can pull it away from the typical value.

The middle value when the data is arranged in order; with an even number of values it is the mean of the two middle ones. It is not affected by extreme values.

The value or category that occurs most often in a set of data. A data set can have one mode, several modes, or no mode at all if every value occurs equally often.

The largest value minus the smallest value in a data set. It is simple to calculate but depends only on the two extremes, so a single unusual value can make it misleading.

Values that split ordered data into four equal parts. The lower quartile is one quarter of the way up the data and the upper quartile is three quarters of the way up.

The upper quartile minus the lower quartile. It measures the spread of the middle half of the data and, unlike the range, is not distorted by extreme values.

A measure of how far values typically lie from the mean. A large standard deviation means the data is spread out, while a small one means values cluster close to the mean.

A value that lies far away from the rest of the data. It may be a genuine extreme result or a recording error, and it can strongly affect the mean and the range.

A graph with one variable on each axis where each point represents one item or person. It shows whether the two variables appear to be related and how closely.

The tendency for one variable to increase as the other increases, so the points on a scatter diagram rise from bottom-left to top-right.

A straight line drawn through the middle of the points on a scatter diagram, lying as close as possible to as many points as it can, used to describe the trend and make estimates.

A number between minus one and one describing how closely the points on a scatter diagram follow a straight line. Positive values show an upward trend, negative values a downward one, and values near zero show no linear pattern.

Using a line of best fit to estimate a value outside the range of data actually collected. Such predictions are risky because there is no evidence that the pattern continues beyond the observed data.

A set of values recorded at regular time intervals, such as sales figures for each month. It is used to identify a long-term direction and any pattern that repeats over time.

The underlying long-term direction of a time series once short-term ups and downs are ignored. It is often shown by a line of best fit or by a moving average.

A regular pattern that repeats over a fixed period, such as sales being higher every December. It is short-term and predictable, and is separate from the longer-term trend.

An average of a fixed number of consecutive values in a time series, recalculated at each point. It smooths out short-term fluctuations so that the underlying trend is easier to see.

A number from zero to one describing how likely an event is, where zero means impossible and one means certain. It can be based on equally likely outcomes, on experiment, or on judgement.

The number of times an event occurs divided by the number of trials. With many trials it gives a good estimate of the probability, and it is used when outcomes are not equally likely.

Two or more events that cannot happen at the same time, such as rolling a three and a five on a single die. Their probabilities add together to give the probability of either happening.

Events where the outcome of one does not change the probability of the other, such as two separate coin tosses. The probability of both happening is found by multiplying.

A list or diagram of every possible outcome of an experiment. Writing it out helps you count the favourable outcomes and work out probabilities accurately.

A branching diagram showing the possible outcomes of two or more events happening in sequence. Probabilities are multiplied along a branch and added across branches to combine outcomes.