How the problems are made
Every business and figure is invented, with a season pattern that makes sense for it: ice creams peak in summer, a ski lodge in winter, a café at the weekend. Every answer is worked exactly and rounded once, where the question says. Moving means with an even number of points are centred, seasonal indices are worked from each year's mean, and forecasts are put back into season with the index. A set code makes the same problems on any device, so a class can share one set or print up to 30 different ones.
An example from set SA5A34
The seasonal indices for ice creams sold at a beach kiosk are 1.51, 0.97, 0.56 and 0.96 for quarters 1 to 4, which add up to 4. To correct for seasonality, each actual figure is divided by its index. Quarter 1's index is above 1, so its figures are reduced, by (1 − 1 ÷ 1.51) × 100 = 33.77…, which rounds to 34%, not by 51%. Quarter 3's index is below 1, so its figures are increased, by (1 ÷ 0.56 − 1) × 100 = 78.57…, which rounds to 79%. Open set SA5A34
What VCAA asks for
The time series part of Data analysis in VCE General Mathematics Units 3 and 4 covers the features of a time series plot (trend, seasonality, outliers and irregular fluctuations), smoothing with moving means and medians, seasonal indices, deseasonalising, and fitting a least squares line to deseasonalised data to forecast. The formula sheet gives seasonal index = actual figure ÷ deseasonalised figure. VCAA's examination reports note that irregular fluctuations are present in every time series plot, and the 2026 NHT Examination 2 report says cycles are not part of the current study design, so these problems never ask about them.
When a seasonal index is worked from several years, VCAA averages each figure divided by its year's mean. The 2025 Examination 2 report also accepted the mean of the season's figures divided by the mean of all the figures, so both answers are marked right here. Rounding happens once, at the end: the 2023 Examination 2 report asks students not to round until the final answer is obtained.
Questions
How do you calculate a 4-point moving mean with centring?
Work out the two 4-point means either side of the point, then take the mean of those two. For day 8, find the mean of days 6 to 9 and the mean of days 7 to 10, then average them. VCAA's 2024 Examination 1 report shows 22% of students chose an uncentred mean instead.
How do you find a missing seasonal index?
The seasonal indices add up to the number of seasons: 4 for quarters, 12 for months, 7 for a seven-day week. Subtract the known indices from that total. If two are missing and one is twice the other, split what is left in the ratio 2 to 1. In VCAA's 2024 Examination 1, 19% gave the smaller index and 7% gave the sum of the two.
What does a seasonal index of 1.2 mean?
That season's figures are typically 20% above the seasonal average. An index of 0.75 means 25% below it. An index of 1 means the season is just average.
How do you deseasonalise a figure?
Divide the actual figure by the season's index: deseasonalised figure = actual figure ÷ seasonal index. So an index of 1.75 reduces the figure by (1 − 1 ÷ 1.75) × 100 = 43%. In VCAA's 2025 Examination 1, half of students chose 43%, while 23% chose 75%.
How do you forecast with a trend line and a seasonal index?
Number the periods 1, 2, 3 and so on from the first one in the data, and put the period number of the forecast into the least squares line to get a deseasonalised forecast. Then reseasonalise it: multiply by that season's index to get the forecast of the actual figure.
How do you find a moving median?
Take the values with the point in the middle (3 for a 3-median, 5 for a 5-median), put them in order and take the middle one. In VCAA's 2023 Examination 1 report, a common wrong answer for the median of a series was the middle value before sorting.
Sources, checked 28 October 2026: VCAA VCE Mathematics Study Design, from 2023 (Word); VCAA General Mathematics past examinations and reports, including the examination reports for 2023 Examination 1, 2023 Examination 2, 2024 Examination 1, 2025 Examination 1, 2025 Examination 2 and 2026 NHT Examination 2 (Word).