GCSE Statistics Key Terms & Vocabulary

Bivariate data

collected as pairs of values, e.g. height and distance jumped for each student.

Categorical data

data that can be organised into non-overlapping categories.

Census

time consuming and expensive, and is unsuitable when testing destroys or uses up the items.

Class width

the difference between the upper and lower boundaries of a class interval; Edexcel expects students to know class width.

Cluster sampling

named in the Edexcel 1ST0 guidance (1c.03) but not in the AQA 8382 specification.

Confidentiality

a constraint because people may not be willing to reveal confidential information, such as their salary.

Ethical issues

a constraint because the well-being of any participants must always be protected.

Control group

given no treatment (a placebo) or the existing standard treatment, so the new treatment can be compared against it.

Explanatory (independent) variable

the one that may affect the response (dependent) variable.

Extraneous variable

any variable, other than the one being investigated, that could affect the results (OpenStax calls such variables lurking variables: additional variables that can cloud a study).

Laboratory experiment

conducted under highly controlled conditions.

Multivariate data

collected in sets of more than two values; it is Higher-tier content.

Open questions

more demanding than closed questions both to answer and to process, so their answers take longer to analyse.

Opportunity samples

likely to be unrepresentative: people asked together may be in family or friendship groups, and not everyone has a chance to be asked.

Ordinal data

categorical data that can be written in order, e.g. small, medium, large.

Pilot study

a small test run of a questionnaire carried out before the main survey; it is not carried out on the entire population. [Edexcel 1H ER Nov 2021 Q1; Edexcel spec 1d.03 guidance (rationale behind pilots); ABS Questionnaire Design (pilot tests)] Board note 2026-10-22: Edexcel only; pilot studies are not named in the AQA 8382 spec or 2021-2023 AQA papers, mark schemes and reports.

Pilot study

used to check that questions are understood, so problems can be fixed before the main survey. [Edexcel 1H ER Nov 2021 Q1] Board note 2026-10-22: Edexcel only (see pilot-def).

Population

the whole set of things you are interested in.

Primary data

data collected by the person carrying out the research.

Random response technique

used for sensitive questions because people are more likely to answer truthfully.

Random response technique

named in Edexcel 1ST0 Higher guidance (1d.03) and not in AQA 8382.

Raw data

data in exactly the form in which it was collected.

Reliability

the extent to which something gives consistent results: repeated measurements yield similar results.

Sample

a subset of the population which is used to collect data from.

Sample

quicker and cheaper than a census and gives less data to analyse, but it might not represent the population and could introduce bias.

Secondary data

data collected previously by someone else, e.g. an organisation, rather than by you.

Stratification

not a method of sampling but a method which may be used before sampling takes place.

Stratifying

appropriate when a characteristic such as gender may affect the variable being studied, so each group should be represented.

Stratum sample sizes

rounded to the nearest whole number; the strata 24, 65, 57 and 14 with a sample of 20 give 3, 8, 7 and 2.

Validity

the extent to which something measures what it is supposed (intended) to measure.

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Action lines

set at plus or minus 3 standard deviations of the sample mean from the expected (target) value. [Edexcel 1ST0 2g.02 guidance; AQA 8382 E11b, E11c] Board note 2026-10-22: the 3 sd placement is stated only in Edexcel 2g.02 guidance; no AQA spec text or 2021-2023 AQA paper states it, so cards testing it are Edexcel only.

Association

the general term for a relationship between two variables; correlation describes a linear association.

Price indices

based on a large basket of goods and services typically bought by households, with weights reflecting the importance of each item in the basket.

CPIH

the CPI including owner occupiers' housing costs (and Council Tax).

Death rate

found the same way: (number of deaths / total population) x 1000.

Cyclic pattern

a rise and fall that is not of a fixed period (often linked to economic cycles and usually lasting at least 2 years), whereas seasonal variation always has a fixed, known period.

Double mean point

(x-bar, y-bar), the mean of the x-values and the mean of the y-values.

Explanatory (independent) variable

plotted on the x-axis and the response (dependent) variable on the y-axis.

Extrapolation

estimating a value outside the range of the data; it is unreliable because the trend may not continue.

4-point moving average

(x1 + x2 + x3 + x4) / 4, then the window moves on one value at a time.

Gradient b

the change in y for each one-unit increase in x, e.g. 19.61 means weight rises by 19.61 g for each 1 cm of length.

Intercept a

the predicted y when x = 0; it is often not meaningful because x = 0 lies outside the data (e.g. a bone length of 0 cm).

Interpolation

estimating a value within the range of the data; it is reasonably reliable when correlation is strong.

Tied ranks

not tested in Spearman calculations, and values found using calculator functions are permissible.

Almost all sample

fall inside the action lines, and only about 1 in 20 fall outside the warning lines. [Edexcel 1ST0 2g.02 guidance] AQA basis: E11b 'approximately 95% of the data lie within two standard deviations of the mean' with warning lines at 2 sd (AQA 8382/2H June 2023 Q13(b)).

Crude birth rate

the number of live births in a year per 1,000 mid-year population.

Capture-recapture assumes enough time

allowed for marked animals to mix back into the population before the second sample.

Quality assurance control charts

used, for example, in a manufacturing process to test that measurements stay within allowable limits.

Regression line

written in the form y = a + bx, where b is the gradient and a is the y-intercept.

Scatter diagram

used to display bivariate data: two variables measured on each item.

Seasonal variation

a pattern that repeats over a fixed period such as the four quarters of each year, e.g. sales always highest in quarter 2.

Correlation

described by inspection as strong (points close to a straight line) or weak (points widely scattered about a line).

Trend

the general long-term increase or decrease of a time series; it can be identified by inspection or by calculating moving averages.

Warning lines

set at plus or minus 2 standard deviations of the sample mean from the expected (target) value. [Edexcel 1ST0 2g.02 guidance; AQA 8382 E11b, E11c] AQA examines this placement: AQA 8382/2H June 2023 Q13(b) 'The warning limit lines for the machine are drawn at x + 2y and x - 2y'.

Weighted index numbers

Higher tier content on both AQA and Edexcel.

Zero (no) correlation

there is no linear pattern between the two variables.

AQA treats correlation values of 0.6 or above (or -0.6 or below) as strong, 0.2 up to but not including 0.6 (or -0.2 down to but not including -0.6) as weak, and values strictly between -0.2 and 0.2 as no correlation; "moderate" is not required.

The base year always has an index number of 100.

If a sample value lies between a warning line and an action line, another sample is taken straight away.

A chain base index number compares each value with the value one period earlier: (this year's value / last year's value) x 100.

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Bars

read as proportional to their values, so truncating a bar chart's axis distorts the relative proportions.

Box plots

compared using the medians (average) and interquartile ranges (spread), interpreted in context.

Box plot

drawn from five values: lowest value, lower quartile, median, upper quartile and highest value.

Larger interquartile range

the data are more spread out and less consistent.

Cumulative frequency

the running total of the frequencies.

Comparative pie charts

more appropriate than ordinary pie charts when the totals being compared are different.

Very common error

plotting frequency instead of frequency density.

Frequency polygon

appropriate for continuous grouped data and shows the shape of the distribution.

Frequency polygon points

joined with straight lines; freehand lines are not credited.

Frequency

found from a sector angle as angle ÷ 360 × total frequency.

Breaking the y-axis

acceptable on a line chart when necessary, because line charts are not read like bar charts, but the break should be made clear.

Pie charts

appropriate for comparing proportions (shares of a whole), such as the proportion of brides in each age group.

Leaves

put in order so that key values such as the median and quartiles can be identified.

Total frequency

the sum of all the frequencies, not the number of categories.

3D representations can distort the sizes of parts, so they should be interpreted with care and avoided when drawing charts.

A common error is to find the angle as 360 divided by the frequency.

The sector angles of a pie chart must add up to 360 degrees.

In a histogram the area of each bar represents the frequency, not its height.

A back-to-back stem and leaf diagram shows two data sets either side of one shared stem so they can be compared.

In a back-to-back diagram the key must cover both sides; for example 4 | 9 | 0 means 94 on the left side and 90 on the right side.

A bar line (vertical line) chart displays discrete data such as counts.

The box runs from the lower quartile to the upper quartile, so its length is the interquartile range and it holds the middle 50% of the data.

The line inside the box marks the median, the average shown on a box plot.

The whiskers end at the lowest and highest values, so the range is highest value minus lowest value.

If the median is closer to the lower quartile than the upper quartile (median - LQ < UQ - median), the data are positively skewed.

A box plot shows spread and symmetry, but a histogram shows the shape of a distribution in more detail (for example whether it is bell shaped).

A cumulative frequency graph can never have a negative gradient: it only rises or stays level.

The number of values above a given value is the total frequency minus the cumulative frequency at that value.

The median, lower quartile and upper quartile are estimated by reading across at 50%, 25% and 75% of the total frequency.

Discrete data use a cumulative frequency step polygon; AQA gives no credit for answers from other cumulative frequency diagrams in that case.

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Geometric mean

only used in an exam when the word "geometric" appears; otherwise "mean" means the arithmetic mean.

Identifying outliers by inspection

Foundation content; identifying them by calculation is Higher tier.

Interdecile range

the 90th percentile minus the 10th percentile, so it covers the middle 80% of the data.

Interpercentile range

one percentile minus another, for example the 10th to 90th or 2.5th to 97.5th interpercentile range.

Interquartile range

written IQR and is the upper quartile (UQ) minus the lower quartile (LQ).

Large outlier

a value greater than UQ + 1.5 x IQR.

Small outlier

a value less than LQ - 1.5 x IQR.

Arithmetic mean

the sum of the values divided by the number of values; for a frequency table, mean = sum of fx divided by sum of f.

Mean

appropriate when all the data should be taken into account, and it allows a standard deviation to be calculated.

Median

the middle value when the data are in order; with an even number of values it is the mean of the two middle values.

Median

more appropriate than the mean when data are skewed, because it is not affected by extreme values.

Mode

the most common value; for grouped data the modal class (modal group) is the class with the highest frequency.

Mode

appropriate when data are non-numeric or when considering demand, such as which clothing size to stock.

Deciding whether there

outliers is marked M1 for LQ - 1.5 x IQR or UQ + 1.5 x IQR, M1 for both limits, and A1ft for "Correct evaluation of their correct" calculations with "the correct decision".

Skewness

marked M1 for a method using 3(mean - median) / standard deviation and A1 for the value; describing the skew earns "B1 for identifying positive skew" ("B0 for positive correlation") and B1 for a correct interpretation such as the mean being greater than the median, with "B0 for an incorrect interpretation given".

Pth percentile

the value below which p% of the data lie; for example, the 75th percentile means 75% of the values are at or below it.

Alternative formula

standard deviation = square root of (sum of x squared / n - (sum of x / n) squared).

Standard deviation formulae

given in the exam (on the formulae sheet or in the question); students need not memorise them.

Standard deviation

Higher tier content on both AQA and Edexcel.

Standard deviation

paired with the mean when comparing data sets (median pairs with IQR).

Value

also an outlier if it lies outside mean plus or minus 3 standard deviations.

Determining skewness by inspection

Foundation content; by calculation it is Higher tier.

Skewness formula

given in the exam when it is needed.

Weighted mean

used when the values do not all have equal importance, so each value is multiplied by its weight before averaging.

Students must understand the effect on the mean, mode and median of adding or withdrawing a member of the population or sample.

AQA quartile questions use data sets with n values where n is one less than a multiple of 4, so the quartiles are actual data values.

Outlier boundaries may need to be calculated so that outliers can be identified and marked separately on a box plot.

Students must comment on outliers with reference to the original data, deciding whether they should be kept or removed.

Comparisons of averages must be context-based interpretations (for example, "on average students at Britstone scored higher"), not just a statement that two numbers differ.

Edexcel may use any value of n, so quartiles may not be data values; any clear method is accepted.

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Absolute risk

the probability of the event in one group, found from collected data as number affected / number in the group.

Relative risk from counts

marked M1 for one risk (15/50 or 32/80), M1 for a complete attempt at relative risk (one risk divided by the other) and A1 for 0.75; the interpretation mark is B1ft, with "B0 if no relative risk found".

Events

mutually exclusive if they cannot occur at the same time: they share no outcomes and P(A and B) = 0.

Normal distribution

symmetrical with a bell shape.

Probabilities

compared on a 0 to 1 (or 0% to 100%) scale and can be written as fractions, decimals or percentages; no probability is below 0 or above 1.

Relative risk

a ratio, so it can be large even when both absolute risks are tiny (0.002 vs 0.001 gives a relative risk of 2); the absolute risks are needed to judge how big the risk actually is (e.g. a 1 in 1,000 risk rising eightfold is still only 8 in 1,000).

Sample space

the set of all possible outcomes; it can be shown by listing, a table (sample space diagram), a tree diagram or a Venn diagram.

P(at least one) = 1 - P(none), since "none" and "at least one" cover every outcome with no overlap.

Examiners want bias judged by relating experimental frequencies to the theoretical probabilities, not by the look of the spinner.

The probability that all n trials are successes is p to the power n, e.g. 0.99 to the power 5 = 0.951 (3 sf).

A binomial model needs a fixed number of trials, only two possible outcomes on each trial, a constant probability of success, and independent trials.

P(exactly r successes) = number of orders x p^r x (1 - p)^(n - r), e.g. n = 3, p = 0.2: P(exactly 1) = 3 x 0.2 x 0.8 x 0.8 = 0.384.

Edexcel: the mean of a binomial distribution B(n, p) is np.

AQA questions use n no greater than 5; Edexcel questions use n no larger than 10.

The distribution of the number of successes in a fixed number of independent trials, each with the same probability of success, is called the binomial distribution.

Edexcel may write a binomial distribution as B(n, p), where n is the number of trials and p the probability of success; AQA does not use this notation.

The number of orders giving r successes in n trials is a binomial coefficient (a row of Pascal's triangle), e.g. 6 orders for 2 successes in 4 trials.

When p = 0.5 the binomial distribution is symmetrical, so for n = 5, P(1 success) = P(4 successes).

Drawing without replacement from a small group breaks the binomial conditions, because the probability of success changes from trial to trial and trials are not independent.

Comparing experimental results with theoretical predictions can identify possible bias, e.g. whether a set of dice rolls suggests the dice is fair.

Conditional probability: P(B | A) = P(A and B) / P(A); the formula must be known.

From a two-way table or Venn diagram, P(B | A) uses only the cases where A happened as the denominator.

Higher tier: differences between experimental and theoretical values are commented on in terms of possible bias; formal significance tests are not required, and a small difference can arise by chance.

A set of events is exhaustive if at least one of them has to occur whenever the experiment is carried out (they cover every possible outcome).

Expected frequency of a characteristic = probability x number in the sample or population (or number of trials).

An estimated probability (relative frequency) can be used in the same way to predict a frequency, e.g. 0.23 x 500 = 115.

For a fair dice rolled 600 times the theoretical expectation is 600 x 1/6 = 100 of each score, so a result far from this suggests bias.

Higher (Edexcel): the general addition law is P(A or B) = P(A) + P(B) - P(A and B), e.g. 0.75 + 0.4 - 0.24 = 0.91.

Multiplying probabilities over repeated periods assumes independence, e.g. 0.75 x 0.75 for two months assumes selling in one month is independent of selling in another.

To test independence, compare P(A and B) with P(A) x P(B), or compare P(A) with P(A | B); equal values mean independent.

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The data collection stage requires recognising constraints in sourcing data: designing primary collection methods, researching secondary sources, acknowledging sources and recognising where sensitivity may limit data availability.

Students must show the importance of clear and concise communication of findings and an awareness of the target audience.

Evaluation and review means identifying weaknesses in approach or representation, suggesting improvements, and refining the process to clarify the initial hypothesis further.

The AQA specification lists five stages of the statistical enquiry cycle: initial planning, data collection, data processing and presentation, interpretation of results, and evaluation and review.

Results must be interpreted in the context of the problem: analysing diagrams and measures, reaching conclusions that relate to the hypothesis, making inferences or predictions and discussing reliability.

Edexcel states that statistical conclusions are developed through an iterative process of testing and refinement, which is why the enquiry is drawn as a cycle.

In an Edexcel 2023 question critiquing a plan, credit was given for points such as repeating each jump and using the mean, controlling extraneous variables, and planning what to do with outliers.

Initial planning includes defining a question or hypothesis, deciding what data to collect and how to collect and record it, and developing a strategy for processing and representing the data, giving reasons.

Processing and presentation covers organising data, generating diagrams and visualisations, and generating statistical measures, including understanding how technology can automate processing.

Both specifications expect students to understand that technology (spreadsheets, statistical software) can be used to organise and process data and to generate diagrams.