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Seasonal indices
Same idea, four ways to study it. Tap a style and find the one that clicks for you. 📺 Prefer to watch? Videos are on the lesson page.
📅 A seasonal index says how far a season sits above or below average. SI = season mean ÷ overall mean. To strip the season out: deseasonalise (÷ SI). To put it back for a forecast: × SI.

What it is

A seasonal index is a number that says how much a particular season is above or below the yearly average. 1.4 means that season is typically 40% above average, 0.6 means 40% below. The indices always average to 1 (or sum to the number of seasons).

The three moves

Seasonal index = season mean ÷ overall mean

Deseasonalise (remove the season to see the true trend): actual ÷ SI.

Forecast / reseasonalise (put the season back onto a trend value): trend × SI.

Worked example

Season means: Summer 154, Autumn 110, Winter 66, Spring 110. The overall mean is 110. Find each seasonal index.

SeasonMean ÷ 110SI
Summer154 ÷ 1101.4
Autumn110 ÷ 1101.0
Winter66 ÷ 1100.6
Spring110 ÷ 1101.0

Check: 1.4 + 1.0 + 0.6 + 1.0 = 4 ✓ (they sum to the number of seasons, so they average to 1).

Watch out

Deseasonalise = ÷ SI. Forecast = × SI. Mixing these up is the classic lost mark.
• Seasonal indices must add to the number of seasons (4 for quarters, 12 for months).
• SI above 1 = a busy season, below 1 = a quiet season.
• A missing index = (number of seasons) − (sum of the others).

Seasons against the average line

1.0 1.4Summer 1.0Autumn 0.6Winter 1.0Spring

Summer sits 40% above the dashed average line (1.4), winter 40% below (0.6), autumn and spring are bang on average (1.0). They balance out around 1.

The two directions

Deseasonalise
actual ÷ SI
strip the season out
Forecast
trend × SI
put the season back

Going in to see the true trend, divide. Coming back out to predict a real figure, multiply.

Warm up first

Don't read yet, just have a go in your head:

SI = 1.2. Above or below average, and by how much?
20% above average.
To deseasonalise, do you multiply or divide by the SI?
Divide. Deseasonalise = actual ÷ SI.
Quarterly indices 1.5, 1.1, 0.7, and one missing. Find it.
They sum to 4. 4 − (1.5 + 1.1 + 0.7) = 4 − 3.3 = 0.7.

Faded example: find the seasonal indices

Rung 1 · watch one done fully

Summer mean 154, overall mean 110. SI = 154 ÷ 110 = 1.4 (40% above average).

Rung 2 · you fill the gaps

Winter mean 66, overall mean 110. SI = 66 ÷ 110 = ? → that's ?% below average.

Check my gaps
0.6, so 40% below average.
Rung 3 · all you

Winter's actual sales were 84, and winter's SI is 0.6. Deseasonalise this figure. Check below.

Check my answer
Deseasonalise = actual ÷ SI = 84 ÷ 0.6 = 140. (Divide, because we're removing the season.)

Exam-style stretch: forecast

The trend predicts a value of 120 for next summer, and summer's SI is 1.4. Forecast the actual summer figure.

Show the working
Forecast = trend × SI = 120 × 1.4 = 168. (Multiply, because we're putting the busy season back on.)

Say it back

In one sentence, out loud: when do you divide by the seasonal index, and when do you multiply?

⚡ Seasonal indices, one look

Seasonal indexseason mean ÷ overall mean
SI > 1busy season (e.g. 1.4 = 40% above average)
SI < 1quiet season (e.g. 0.6 = 40% below)
They sum tothe number of seasons (4 quarters, 12 months)
Deseasonaliseactual ÷ SI  (strip the season out)
Forecasttrend × SI  (put the season back)
Example154 ÷ 110 = 1.4 · deseason 84 ÷ 0.6 = 140
Trap÷ to deseasonalise, × to forecast (don't swap)