Medium2 marksStructured
Statistical Measures and Calculationstime seriesmoving averagesmoothing dataHigher

AQA GCSE · Question 07.3 · Statistical Measures and Calculations

YearNumber of sunspots197019801990200020102020050100150200250300Source: SpaceWeatherLiveFrom Jan 1965toJan 2020

There are variations in the number of sunspots seen per month throughout the year. How could you smooth out these variations?

How to approach this question

The question asks how to "smooth out" variations in time series data. What is the statistical technique used for this purpose? It involves calculating an average over a specific time period that "moves" along the data.

Full Answer

By calculating and plotting moving averages. For example, one could calculate a 12-month moving average to smooth out the monthly/seasonal variations within each year.
To smooth out short-term fluctuations (like monthly variations) in time series data and highlight longer-term trends or cycles, we use **moving averages**. A moving average is calculated by taking the average of a set of data points over a specific period. For example, to smooth monthly data, a 12-month moving average is often used. You would calculate the average for Jan-Dec, then Feb-Jan, then Mar-Feb, and so on. Plotting these moving averages creates a smoother line that makes the underlying cyclical pattern clearer.

Common mistakes

✗ Suggesting drawing a line of best fit, which is used for scatter graphs showing correlation, not for smoothing time series data.\n✗ Being too vague, e.g., "find the average". You need to specify *moving* averages.

Practice the full AQA GCSE Statistics Higher Tier Paper 2

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