SEASONAL INDICES
A seasonal index is a measure of how a particular season compares with the average season.
Consider the monthly seasonal indices for unemployment given in the table
below:
Seasonal indices are calculated so that their average is 1. This means that
the sum of the seasonal indices equals the number of seasons. Thus, if the
seasons are months, the seasonal indices add to 12. If the seasons are quarters,
then the seasonal indices would add to 4, and so on. January has seasonal index
of 1.1which means, January’s unemployment is 10% above average.
September’s unemployment is 15% less than average.
Deseasonalising is the process that is used to remove the seasonal effects from a set of data.
This allows any underline trend to be made clearer.
We can use seasonal indices to deseasonalise time series. To calculate
deseasonalised data, each entry is divided by its seasonal index as follows.
Deseasonalising data
Example: Deseasonalise the quarterly sales figures of Summer Year1 using the
data and seasonal indices tables below.
Solution: Deseasonalised data for ‘Summer 1’ = Summer 1 data
=
Summer seasonal index
920 = 893
1.03
Calculating seasonal indices
Example: Mikki runs a shop and she wishes to determine quarterly seasonal indices
based on her last year’s sales, which are shown in the table below.
Solution: Using the above formula to find the seasonal index
seasonal index = value of the quarter
quarter average
Find the quarter average
quarter average = 920 + 1085 + 1241 + 446 = 923
4
Find the seasonal index of each season
seasonal index Summer = 920 = 0.997
923
seasonal index Autumn = 1085 = 1.176
923
seasonal index Winter = 1241 = 1.345
923
seasonal index Spring = 446 = 0.483
923
Calculating seasonal indices (several years’ data)
Suppose that Mikki has in fact three years of data, as shown. Use the data to
calculate seasonal indices, correct to two decimal places.
Solution: The seasonal average of year 1 was found previously
Find the quarter average for year 2
quarter average year 2 = 1035 + 1180 + 1356 + 541 = 1028
4
Find the seasonal index of each season
seasonal index Summer = 1035 = 1.007
1028
seasonal index Autumn = 1180 = 1.148
1028
seasonal index Winter = 1356 = 1. 319
1028
seasonal index Spring = 541 = 0.526
1028
Find the quarter average for year 3
quarter average year 2 = 1299 + 1324 + 1450 + 659 = 1183
4
Find the seasonal index of each season
seasonal index Summer = 1299 =1.098
1183
seasonal index Autumn = 1324 = 1.119
1183
seasonal index Winter = 1450 = 1.226
1183
seasonal index Spring = 659 = 0.557
1183
To find the seasonal indices of the 3 years we need to find the average seasonal index
of each season.
QUESTIONS
1 The table below shows the monthly sales figures and seasonal indices (for January to
November) for a product produced by the U-beaut company.
a Complete the table by calculating the missing seasonal index.
b Interpret the seasonal index for
i February
ii August
2 The table below shows the quarterly newspaper sales of a corner store for Year 1. Also
shown are the seasonal indices for newspaper sales for the first, second and third quarters.
Complete the table.
3 Each of the following data sets records monthly sales ($000s). Use the data to determine
the seasonal indices for the 12 months. Give your results cor rect to two decimal places.
Check that your seasonal indices add to 12.
4 The number of waiters employed by a restaurant chain in each quarter of one year, along
with some seasonal indices which have been calculated from the previous year’s data, are
given in the following table.
a What is the seasonal index for the second quarter?
b The seasonal index for Quarter 1 is 1.30. Explain what this mean in terms of the average
quarterly number of waiters.
c Deseasonalise the data.
5 The following table shows the number of students enrolled in a 3-month computer systems
training course along with some seasonal indices which have been calculated from the
previous year’s enrolment figures. Complete the table by calculating the seasonal index for
spring and the deseasonalised student numbers for each course.
6 The following table shows the monthly sales figures and seasonal indices (for January to
December) for a product produced by the VMAX company.
a Complete the table by:
i calculating the missing seasonal index
ii evaluating the deseasonalised sales figures
b The seasonal index for July is 0.90. Explain what this means in terms of the average
monthly sales.
ANSWERS
1a 1.0
bi In general, in February, monthly sales are 30% more than in an average month.
Ii In general, in August, monthly sales are 30% less than in an average month.
2
3
4
b In Quarter1therestaurantchainemploys30% more waiters than the number employed in
an average quarter.
5
6
c In July the VMAX company records 10% fewer sales than in an average month.