Advanced Higher Statistics: the 2027 exam, 2026 grade boundaries and practice

The Advanced Higher Statistics exam in 2027

Both papers have short-answer and extended-response questions. The course assessment is graded A to D on the total of the two papers (course specification, version 5.0; Exam Timetable 2027, version 02). The recommended entry is Higher Mathematics. The formulae and tables are in the booklet: see our Advanced Higher Statistics formula sheet.

What Advanced Higher Statistics covers

• Exploratory data analysis. Tables, dot plots, stem-and-leaf diagrams and box plots, and spotting outliers.
• Probability. Set notation, the addition and multiplication laws, conditional probability and Bayes' theorem.
• Random variables. Discrete distributions, the laws of expectation and variance, and the uniform, binomial and Poisson distributions, with the normal distribution for continuous data.
• Inference. Confidence and prediction intervals, hypothesis tests for means and proportions, chi-squared tests, and Wilcoxon and Mann-Whitney tests.
• Modelling. Correlation and least squares regression, and control charts with the Western Electric Company rules.

The papers give computer output, such as p-values and regression lines, and ask you to interpret it.

Advanced Higher Statistics grade boundaries

In 2026, out of 120 marks, an A needed 82 (68%), a B 70, a C 59 and a D 47. Of 187 candidates, 36.9% got an A. Entries rose from 176 in 2025. Both papers were more demanding than expected, and that was taken into account (course report 2026).

With a small entry, the shares move a lot from year to year. As a guide, Qualifications Scotland aims for a C at about 50% and an A at about 70% (how National Courses are graded).

Advanced Higher Statistics practice questions

Every question below is our own.

1. Expectation and variance

X has mean 4 and variance 9. Y is independent, with mean 5 and variance 16. For 2X − Y, the mean is 2 × 4 − 5 = 3. The variance is 2² × 9 + 16 = 52, because variances add even for a difference, so the standard deviation is √52 = 7.21.

2. Bayes' theorem

2% of items are defective. A test flags 95% of defective items and wrongly flags 4% of good ones. Given a flag, what is the probability the item is defective?

3. Binomial and the table

X is B(10, 0.3). Find P(X ≥ 5). The cumulative table gives P(X ≤ 4) = 0.8497, so P(X ≥ 5) = 1 − 0.8497 = 0.1503.

Practise normal distribution questions in the Probability course, then press Mark.

Where candidates lose marks

From the 2026 course report:

• Prediction and confidence intervals. Many did not use "individual" for the prediction interval and "mean" for the confidence interval, or the phrase "95% of the time".
• Conditions for a test. Most stated the condition on expected frequencies but not why the data failed it.
• Comparing p-values. Most did not clearly compare each p-value to the significance level.
• Continuity correction. Many did not use it correctly or did not state the z-value.
• Interpreting slopes. Many talked about the strength of a correlation when asked about the difference in gradients.
• The word "skew". It is not in the specification, and many used it for distribution shape.

Use a daily paper as a short timed prelim

Many schools set an Advanced Higher prelim in winter: see our prelims guide. There is no daily paper for Advanced Higher Statistics, so use the daily paper for Higher Applications of Maths, the closest statistics track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full SQA paper and not written by SQA.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper as a timed mock, mark it, and the worked answers show where the marks were. We do not publish official or past paper answers.

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Scotland · Advanced HigherAdvanced Higher Statistics grade boundaries 2025 (SQA)SQA's 2025 Advanced Higher Statistics grade boundaries out of 120, with A at 82 and C at 56, the fall from 2024 and what your mark earns.