seasonal index

Also called: seasonality index, seasonally adjusted

A month’s value divided by the average month: 9,620 lessons in a year that averages 7,400 a month gives an index of 1.30. Dividing by the index removes the season.

Many businesses have strong and weak months: exam season, summer holidays, a September restart. A seasonal index says how a month compares with a typical one:

$\text{index}_m = \frac{\text{value in month } m}{\text{average month}}$

An index of 1.30 means 30% above an average month, 0.65 means 35% below. Over a year the indexes average to 1.

The index has two uses. It tells you whether a strong month is growth or just the season, and it lets you seasonally adjust a figure: divide the actual value by its month’s index to see what a typical month would have looked like. Compare adjusted figures, or the same month across years, rather than raw neighbouring months.

Example

A school averages 7,400 lessons a month over the year.

May brings 9,620: index 9,620 ÷ 7,400 = 1.30.
June brings 6,650 with an index of 0.95: adjusted, 6,650 ÷ 0.95 = 7,000, a slightly below-average month.

Common mistakes

Reading a seasonal peak as growth. Compare with the same month last year or adjust first.
Multiplying by the index to adjust. Divide by it.
Building indexes from one year only. One unusual year makes the index noisy.

Learn it in the course

Typical value and position: mean, median, quartiles · Mean, median, mode and trimmed mean, quartiles, percentiles and the IQR (two ways to compute them), a seasonal index, and the cumulative share curve.