Deseasonalise and reseasonalise values practice questions | General Mathematics (Year 12, VCE Units 3 & 4)

Adjusting for seasonality

A seasonal index is a multiplier that describes how a season compares with the average season. Remove that multiplier by division and restore it by multiplication

D=\frac{A}{I},\quad A=D\times I,\quad M=\frac{1}{I}

Remove the seasonal effect Divide an actual value A by its seasonal index I \(\displaystyle D=\frac{A}{I}\)
Restore the seasonal effect Multiply a deseasonalised value D by the applicable seasonal index \(\displaystyle A=D\times I\)
Compare the index with one An index above one is above the average season; an index below one is below the average season \(\displaystyle I=1.20>1\Rightarrow20\%\text{ above average}\)
Find a correction percentage Use the removal multiplier 1 divided by I, then compare it with one \(\displaystyle I=0.80\Rightarrow\frac{1}{I}=1.25\Rightarrow25\%\text{ increase}\)

Worked example

A community pool records 720 visits in a quarter with seasonal index 1.20. Find the deseasonalised value, then reseasonalise it for a quarter with index 0.80

A_1=720,\quad I_1=1.20,\quad I_2=0.80

\(\displaystyle D=\frac{720}{1.20}=600\)Divide the actual value by its index to remove the first seasonal effect
\(\displaystyle A_2=600\times0.80=480\)Multiply the deseasonalised value by the second index to restore seasonality
\(\displaystyle \text{final actual value}=480\text{ visits}\)The reseasonalised value is 480 visits

Common mistakes

Multiplying when deseasonalising

✕\(\displaystyle D=720\times1.20=864\)✓\(\displaystyle D=\frac{720}{1.20}=600\)

Multiplying by the index applies the seasonal multiplier instead of removing it

Dividing when reseasonalising

✕\(\displaystyle A=600\div0.80=750\)✓\(\displaystyle A=600\times0.80=480\)

Reseasonalising restores the seasonal multiplier, so multiply the deseasonalised value by the index

Subtracting the index from one as the multiplier

✕\(\displaystyle D=720\times\left(1-1.20\right)=-144\)✓\(\displaystyle D=\frac{720}{1.20}=600\)

The removal multiplier is the reciprocal of the index; subtracting the index from one does not deseasonalise the value

Difficulty levels

introDirect deseasonalisation uses a terminating result and one stated seasonal index

standardBoth deseasonalising and reseasonalising are used with a stated rounding requirement

challengeA correction percentage or reverse restoration requires an extra direction or inverse step

examA compact choice distinguishes division, multiplication, the reciprocal and the correction direction

Questions about this topic

What does a seasonal index of 1.20 mean?+

The season is typically 1.20 times the average season, which is 20% above the average

Why is division used to deseasonalise?+

The actual value is the deseasonalised value multiplied by its seasonal index, so division by the index reverses that multiplication

How is the percentage correction found?+

Subtract one from the removal multiplier, then multiply by 100. The sign gives the direction and the absolute value gives the percentage magnitude

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 12, VCE Units 3 & 4, General Mathematics, chapter 5: Time series

In this chapter

Construct and read a time series plot Identify qualitative features in a time series Calculate moving means Moving median smoothing Select and compare smoothing methods Interpret and complete seasonal indices Deseasonalise and reseasonalise values Calculate seasonal indices from complete cycles Fit a time trend and forecast