S2 Data presentation and interpretation — notes on one page

Every Edexcel A-level Maths 9MA0 specification point in S2, read straight through: 4 points with definitions, explanations, mark-scheme wording and worked examples. Practice questions are in the printable question pack.

Checked against Edexcel 9MA0 section S2. Review basis: the qualification registry sourced from the Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) specification; registry verification recorded 11 July 2026.

How this checking works

S2.1 · Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency; connect to probability distributions.

In a histogram, frequency is proportional to bar area and frequency density is $\frac{\text{frequency}}{\text{class width}}$ ; unequal class widths make bar height alone misleading.
Frequency polygons show class patterns, box plots summarise centre and spread, and cumulative frequency diagrams support estimates of medians, quartiles and counts below a value.
For a continuous probability density histogram, total area is $1$ and the area above an interval is the probability of an observation in that interval.
Read class boundaries and axis scales before calculating.
A common error is to use frequency density as though it were frequency.

In a histogram, bar area represents frequency, so height is frequency density.

Worked example

A cumulative frequency diagram represents $80$ observations. The cumulative frequencies at $x=10$ and $x=20$ are $18$ and $54$ respectively. Estimate the number of observations satisfying $10<x\leq20$ .

1.The cumulative frequency at $20$ counts all $54$ observations up to that value, including the $18$ already counted up to $10$ .
2.Subtract to isolate the interval: $54-18=36$ .

Answer: $36$

Common mistakes

Don't use bar height rather than class width times frequency density to compare histogram frequencies.
Don't read cumulative frequencies directly as class frequencies instead of subtracting the boundary totals.

Exam tip. For cumulative-frequency intervals, subtract the cumulative totals at the two boundaries and respect endpoint inequalities.

S2.2 · Interpret scatter diagrams and regression lines for bivariate data, including recognising distinct sections of the population (regression calculations excluded); interpret correlation informally; correlation does not imply causation.

A scatter diagram shows paired bivariate data; describe the direction and strength of its association and note any outliers or clusters.
A regression line estimates the mean response for a given explanatory-variable value and is most defensible within the observed data range.
Distinct clusters may represent different sections of the population, so one overall correlation or regression line can hide different within-group patterns.
Correlation measures association, not causation; a lurking variable, reverse causation or coincidence may explain the observed relationship.
For $y=ax^n$ , plot $\log y$ against $\log x$ to get gradient $n$ and intercept $\log a$ ; for $y=kb^x$ , plot $\log y$ against $x$ to get gradient $\log b$ and intercept $\log k$ .

Worked example

A scatter diagram of journey distance against journey time contains one cluster for bicycles and a separate cluster for cars. Explain why fitting one regression line to all journeys may be misleading.

1.Identify vehicle type as a grouping variable.
2.Since the relationship between distance and time is likely to differ between bicycles and cars, pooling the groups can produce a line that fits neither group well.
3.Analyse the sections separately.

Answer: The two clusters represent distinct sections of the population with different travel speeds.; A single line may mainly reflect the gap between the clusters rather than either within-group relationship.; Separate regression lines or separate analyses would be more informative.

Common mistakes

Don't extrapolate a regression line far beyond the observed data range.
Don't interpret an overall regression line despite distinct clusters representing different subpopulations.

Exam tip. Before using a regression line, inspect clusters and explain whether one relationship is credible for the whole population.

S2.3 · Interpret measures of central tendency and variation, extending to standard deviation; be able to calculate standard deviation, including from summary statistics.

The mean uses every value, while the median is resistant to extremes; choose a measure that suits the distribution and context.
Range and interquartile range measure spread using endpoints or quartiles; standard deviation measures typical spread about the mean using all observations.
For $n$ data values, use $\sigma=\sqrt{\frac{\sum x^2}{n}-\left(\frac{\sum x}{n}\right)^2}$ unless a different convention is stated.
When groups are combined, add $n$ , $\sum x$ and $\sum x^2$ before recalculating; averaging separate standard deviations is not valid.
Coding data by $y=(x-a)/b$ simplifies calculation, after which transform the statistics back; grouped-data percentiles require linear interpolation within the relevant class.

Worked example

For $20$ observations, $\sum x=310$ and $\sum x^2=5020$ . Calculate the population standard deviation to $3$ significant figures.

1.The mean is $310/20=15.5$ .
2.Hence $\sigma=\sqrt{5020/20-15.5^2}=\sqrt{251-240.25}=\sqrt{10.75}=3.278\ldots$ , so the standard deviation is $3.28$ .

Answer: $3.28$

Common mistakes

Don't average two group means without weighting them by their different sample sizes.
Don't use $S_{xx}/n$ as the standard deviation without taking the square root.

Exam tip. Substitute the stated divisor into the variance formula, keep the square root until the end and check the result is non-negative.

S2.4 · Recognise and interpret possible outliers in data sets and statistical diagrams; select or critique data presentation techniques in context; clean data, including dealing with missing data, errors and outliers.

A common outlier rule flags values below $Q_1-1.5\operatorname{IQR}$ or above $Q_3+1.5\operatorname{IQR}$ , but context should guide the final decision.
Investigate a suspicious value against the original record before correcting or removing it; an unusual valid observation is not automatically an error.
Handle missing data transparently: record how many values are missing, avoid inventing unsupported values and consider whether missingness could bias conclusions.
Choose displays to suit the data and purpose: histograms for continuous grouped data, box plots for comparing distributions, and scatter diagrams for paired variables.

Worked example

A table of package masses contains one blank entry and one value $482$ among values near $48.2$ grams. Describe a defensible way to clean these two entries before analysis.

1.First distinguish a data-entry error from a genuine extreme value by consulting the source.
2.Do not silently divide $482$ by $10$ .
3.The blank contains no observed value, so omit it from calculations unless a justified imputation rule has been chosen, and document the decision so its possible bias is visible.

Answer: Check the original measurement record for both entries.; Correct $482$ to $48.2$ only if the source confirms a decimal-point error; otherwise retain and flag it or exclude it with a stated reason.; Treat the blank as missing rather than replacing it without evidence, and report the reduced sample size or justified imputation method.

Common mistakes

Don't replace every missing value with zero, changing both the centre and spread of the data.
Don't delete an unusual value automatically instead of investigating whether it is an error or genuine observation.

Exam tip. Document separate rules for missing values, transcription errors and plausible outliers before recalculating summaries.