Unit 3 Topic 3 · week 7 · SI = season mean ÷ overall mean · deseasonalise = ÷ SI · forecast = trend × SI
The concept in one sentence: a wiggly line over time is really trend + season stacked together, the seasonal index says how each season compares to a normal one, and you DIVIDE to take the season out or MULTIPLY to put it back in.
The thing that makes it click: SI as "that season's usual share of normal". 1.2 means the season usually runs 20% over a typical period; 0.8 means 20% under. Above 1 is above average, below 1 is below, always.
1 · Prerequisite check (30 seconds)
"Mean of 120, 80, 95, 105?" and "Is 0.8 more or less than 1? By what percent?"
If percent-below wobbles (reading 0.8 as 80% of average vs 20% below), fix it right here with money: "$0.80 for every usual dollar". This single reading error causes most SI mark losses.
2 · The teaching path
Concrete: a kiosk that sells more in summer. Sketch four years of quarterly sales as a wiggly-but-rising line. Ask him to point at the trend and point at the season. He can, everyone can, the decomposition idea is intuitive before it's mathematical
Moving means: smoothing = averaging neighbours to iron out the bumps so the trend shows. Do a 3-point run by hand once (14, 22, 18, 26, 20 → 18, 22, 21.33). The POINT is what to say: smoothing trades detail for trend. (The syllabus also allows the moving MEDIAN, same idea with middle instead of mean, mention it once)
Seasonal index: quarter means 120, 80, 95, 105 → overall mean 100 → SIs 1.2, 0.8, 0.95, 1.05. Then the self-check gift: the four SIs must add to 4
The ÷ out, × back pair, taught as one breath, never separately:
deseasonalise = actual ÷ SI (take the season OUT) · forecast = trend × SI (put the season BACK)
Run the full pipeline once: actual Q1 of 132 → ÷ 1.2 → 110 deseasonalised. Trend predicts 118 for next Q2 → × 0.8 → 94.4 forecast. One page, whole story
Above 1 is above average. Below 1 is below. Every time.
Divide to strip the season out. Multiply to dress it back up.
3 · Misconception catalogue
Looks like
Why brains do it
The fix script
Reads SI 0.7 as "above average"
0.7 is a positive number, positive feels like "up"
The dollar read: "70 cents for every usual dollar. Is that a good quarter?" Then the chant: above 1 above, below 1 below
Multiplies to deseasonalise
Multiplying feels like the default operation
"Deseasonalise means REMOVE the season's effect. The SI inflated it, so divide it back out." Check with sense: a busy season's number should shrink
Uses the trend value as the forecast, forgets the SI
The trend line looks like the prediction machine
"The trend forecasts a NORMAL period. Is Q2 normal? No, it's a 0.8 season. Dress it back up." Forecast = trend × SI
SIs don't sum to the number of seasons and he doesn't notice
No self-check habit
Install the ritual: four quarterly SIs sum to 4 (monthly, 12). Two seconds, catches arithmetic slips for free
Thinks smoothing "deletes data"
The wiggles disappearing feels like losing information
"We're not deleting, we're separating: the wiggle goes in the season bucket, what's left is the trend"
Reads a one-off spike as a seasonal pattern
Any bump looks like a pattern
"Seasonal means it repeats on schedule. Did it happen every summer, or just that one grand final weekend?" (irregular vs seasonal variation)
Uses the wrong quarter's SI when forecasting
Grabs the index of the quarter the trend value came from
"The SI belongs to the season you're PREDICTING, not the one you came from. Which quarter is this forecast for? Use its index"
4 · Questioning ladder
Rung
Ask
Listen for
Recall
"SI of 1.3 means?"
"30% above average", instantly
Do
"Actual 132, SI 1.2. Deseasonalise"
÷, gets 110, can say why he divided
Explain back
"Why divide to deseasonalise but multiply to forecast?"
Any version of out-vs-back-in ("strip it out" / "dress it up")
Transfer
"Trend says 118 for a quarter whose SI is 0.8. Forecast, and explain to the kiosk owner what it means"
94.4 AND a sentence: "Q2 is a quiet quarter, expect below the trend"
5 · How QCAA examines it
The full seasonal run is the classic: compute SIs from a table of means → deseasonalise a figure → forecast from a trend value. It chains, so one early slip cascades: teach the SI sum check as damage control
Interpret-the-SI sentences carry marks ("Q2 sales typically run 20% below the yearly average"), same sentence-frame game as regression
Moving means (or medians): compute a short run and STATE THE PURPOSE (smoothing to reveal trend). Syllabus scope: an ODD number of points only, mean or median. Centring is OUT of scope, skip it entirely
No new formula-book letters here, the three relationships in the banner above are the whole toolkit
6 · Stuck scripts
Above or below 1?
Are we taking the season OUT or putting it BACK?
Do your four indices add to 4?
Would this number make sense to the kiosk owner?
7 · ADHD delivery notes
The ÷ out / × back pair goes on ONE card, never split across pages: it's a single idea with two directions
The pipeline (SIs → deseasonalise → forecast) suits him: it's a procedure, not a puzzle. Frame it as "the same three moves every time"
Real-shop framing (the kiosk, the servo) keeps the numbers meaning something; "would the owner believe this?" doubles as a sense-check habit
This topic pairs naturally with a drills week: the SI reading questions (above/below 1) are pure identification, his format