AQA GCSE Statistics The normal distribution and index numbers: a complete overview of the bell curve, standardised scores and the RPI

What this module demands

This final module brings together the normal distribution, standardised scores and index numbers. AQA tests whether you can use the bell curve and the $68$, $95$, $99.7$ percent rule, standardise and compare scores, and calculate and interpret index numbers such as the RPI. Calculation and interpretation share the marks.

This guide walks through the three topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

The normal distribution

The module opens with the normal distribution: the symmetrical bell-shaped curve, the mean, median and mode all at the centre, the role of the standard deviation in setting the width, and the $68$, $95$, $99.7$ percent rule.

Standardised scores

Standardised scores covers the formula, value minus mean over standard deviation, and using standardised scores to compare results from different distributions, where the higher standardised score is the better relative performance.

Index numbers and the RPI

Index numbers and the RPI covers simple index numbers and the base year, the Retail Price Index and Consumer Price Index, chain base index numbers, and weighted index numbers.

How this module is examined

A typical AQA profile for this module:

• Normal distribution. Applying the $68$, $95$, $99.7$ percent rule and reasoning about symmetry.
• Standardised scores. Calculating a standardised score and comparing two performances.
• Index numbers. Calculating a simple index and interpreting an index value.
• The RPI. Explaining what the RPI and CPI measure and the idea of a weighted index.

Check your knowledge

A mix of recall and calculation questions covering this module. Attempt them under timed conditions, then check against the solutions.

1. What percentage of data lies within two standard deviations of the mean in a normal distribution? (1 mark)
2. A normal distribution has mean $50$ and standard deviation $5$. Between which values do about $68\%$ of values lie? (2 marks)
3. A value of $70$ comes from a test with mean $60$ and standard deviation $5$. Find its standardised score. (2 marks)
4. Two students have standardised scores of $0.8$ and $1.2$. Who did relatively better? (1 mark)
5. A price index is $135$. By what percentage has the price risen since the base year? (1 mark)
6. An item cost $\pounds 40$ in the base year and $\pounds 50$ now. Find its index number. (2 marks)
7. What does the RPI measure? (1 mark)
8. In a normal distribution, where do the mean, median and mode lie? (1 mark)