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Statistical Measures and CalculationsGeometric MeanAveragesPercentage ChangeGCSE

AQA GCSE · Question 13.1 · Statistical Measures and Calculations

Year 2016 2017 2018 2019 2020 Multiplier 1.067 1.013 1.008 1.005 1.126

Maisy has her house valued each year. The table shows the percentage increase in its value, written as a multiplier, over each of the last 5 years. Maisy wants to know the average percentage increase over the 5 years. She works out the arithmetic mean of the percentage increases (6.7%, 1.3%, 0.8%, 0.5%, 12.6%) and gets 4.4%. Maisy has used the wrong method. Name the measure she should have calculated.

How to approach this question

1. **Identify the type of data**: The data consists of multipliers representing percentage increases over time. This is rate of change data. 2. **Recall the appropriate average for rates of change**: The arithmetic mean is used for averaging simple numbers. However, for averaging rates, ratios, or growth factors (like percentage increase multipliers), the geometric mean is the correct measure. 3. **State the correct measure**: The measure Maisy should have calculated is the geometric mean.

Full Answer

Geometric mean
The arithmetic mean is appropriate for finding the average of a set of numbers where each number is independent. However, when dealing with rates of change, such as annual percentage increases, the effect is multiplicative (compound). The correct measure of the average rate of change is the **geometric mean**. The geometric mean is calculated by multiplying all the values (in this case, the multipliers) together and then taking the nth root, where n is the number of values.

Common mistakes

✗ Stating "mean" (too vague). ✗ Suggesting another incorrect average like median or mode.

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