Reading seasonal indices
A seasonal index compares a typical value in one period with the average seasonal value. The value 1 is the reference, so an index above 1 is above average and an index below 1 is below average
- Use 1 as the reference Compare the index with 1 before finding a percentage or direction \(\displaystyle I=1.18>1\Rightarrow\text{above average}\)
- Find an above-average percentage For an index above 1, subtract 1 and multiply the excess by 100 \(\displaystyle 1.24-1=0.24=24\%\)
- Find a below-average percentage For an index below 1, subtract it from 1 and multiply the shortfall by 100 \(\displaystyle 1-0.83=0.17=17\%\)
- Use the seasonal total If there are S seasons, their indices have sum S because their average is 1 \(\displaystyle I_1+I_2+I_3+I_4=4\)
Worked example
A community library has a seasonal index of 0.76 for winter. What does this index indicate about typical winter loans?
- \(\displaystyle 0.76<1\)The index is below the average seasonal index of 1
- \(\displaystyle 1-0.76=0.24\)The shortfall from the average index is 0.24
- \(\displaystyle 0.24\times100\%=24\%\)Typical winter loans are 24% below the average seasonal value
Common mistakes
Difficulty levels
Questions about this topic
Why is 1 the reference for a seasonal index?+
Seasonal indices are scaled so that the average seasonal level is 1. An index of 1 therefore represents the average seasonal value
Why is an index of 1.25 equal to 25% above average rather than 125% above average?+
The index says the typical value is 1.25 times the average. Subtracting 1 from 1.25 gives a difference of 0.25, which is 25%
Why do four seasonal indices add to 4?+
Their average is 1, so the sum of four indices is 4 times 1, which is 4
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