Worked answers

Statistics questions, worked through

The mathematics of uncertainty, distributions, sampling, hypothesis testing and regression. It appears inside Maths A Level, as a standalone qualification, and as a required module in psychology, economics, business and biology degrees.

  • 3 worked answers
  • 3 topics

Correlation and interpretation

Measures of central tendency

Sampling methods and bias

Where Statistics marks actually go

These answers are written around the failure modes below rather than around the topic list. That is deliberate: most students who are stuck in this subject know more content than their grade suggests, and lose marks to one of these instead.

  • Hypothesis testing performed correctly and then concluded wrongly: the arithmetic is fine, the sentence at the end is not
  • Choosing the wrong distribution because the conditions for each were never clearly separated
  • Calculator statistical functions used without understanding, so an implausible answer goes unnoticed
  • Interpreting correlation as causation in exactly the way the mark scheme is waiting for

More on how we teach Statistics, or browse questions in other subjects.

Who these are written for

Students taking it as part of A Level or IB Maths, and undergraduates in social sciences or life sciences who did not expect their degree to contain this much mathematics and now need it to.

How to get something out of a worked answer

Reading one of these is worth very little on its own, which is true of any explanation and is the reason revision by rereading feels productive and mostly is not. The method that works is slightly uncomfortable and takes about ten minutes per question.

Read the question, close the page, and attempt it on paper. Get it wrong if that is what happens: being wrong and then finding out why is the part that sticks. Then read the worked answer and, rather than checking whether your final answer matched, find the exact step where your version diverged from ours. That step is the thing to practise, and it is usually one specific decision rather than a whole topic.

Then find two similar questions from your own materials and do them cold. If the same step goes wrong again, you have found a genuine gap. If it does not, you have just fixed something. The wider method is here.

Why we publish these at all

Because we do not publish reviews or testimonials, and a parent choosing a tutor needs something to judge. Review widgets are cheap and star ratings are unfalsifiable, so we would rather hand you the actual teaching and let you decide whether it is any good. If these explanations are clear, that is the most honest sample of what you would be paying for that we can give you. More on that policy here.

Worked answers in other subjects