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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:

[pic]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.

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Deseasonalising data

Example: Deseasonalise the quarterly sales figures of Summer Year1 using the data and seasonal indices tables below.

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Solution: Deseasonalised data for ‘Summer 1’ = Summer 1 data = 920 = 893

Summer seasonal index 1.03

Calculating seasonal indices

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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[pic]

c In July the VMAX company records 10% fewer sales than in an average month.

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