Aussie Maths & Science Teachers: Save your time with SmarterEd
The table below shows the seasonal indices for the monthly takings of a bistro.
The seasonal indices for months 3 and 6 are missing.
The seasonal index for month 3 is twice the seasonal index for month 6 .
The seasonal index for month 3 is closest to
The time series plot below shows the average monthly ice cream consumption recorded over three years, from January 2010 to December 2012.
The data for the graph was recorded in the Northern Hemisphere.
In this graph, month number 1 is January 2010, month number 2 is February 2010 and so on.
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| Consumption (litres/person) | ||||||||||||
| Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sept | Oct | Nov | Dec |
| 2011 | 0.156 | 0.150 | 0.158 | 0.180 | 0.200 | 0.210 | 0.183 | 0.172 | 0.162 | 0.145 | 0.134 | 0.154 |
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The table below shows the number of visitors to an art gallery during the summer, autumn, winter and spring quarters for the years 2017 to 2019.
The quarterly average is also shown for each of these years.
The seasonal index for summer is closest to
Table 3 below shows the long-term mean rainfall, in millimetres, recorded at a weather station, and the associated long-term seasonal indices for each month of the year.
The long-term mean rainfall for December is missing.
Part 1
To correct the rainfall in March for seasonality, the actual rainfall should be, to the nearest per cent
Part 2
The long-term mean rainfall for December is closest to
The table below shows the long-term monthly average heating cost, in dollars, for a small office.
The seasonal index for April is closest to
The total rainfall, in millimetres, for each of the four seasons in 2015 and 2016 is shown in Table 5 below.
Use the values in Table 5 to find the seasonal indices for summer, autumn and spring.
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Use the appropriate seasonal index from Table 6 to deseasonalise the total rainfall for winter in 2017.
Round your answer to the nearest whole number. (1 mark)
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The quarterly sales figures for a large suburban garden centre, in millions of dollars, for 2016 and 2017 are displayed in the table below.
Using these sales figures, the seasonal index for Quarter 3 is closest to
The table below shows the long-term average of the number of meals served each day at a restaurant. Also shown is the daily seasonal index for Monday through to Friday.
Part 1
The seasonal index for Wednesday is 0.84
This tells us that, on average, the number of meals served on a Wednesday is
Part 2
Last Tuesday, 108 meals were served in the restaurant.
The deseasonalised number of meals served last Tuesday was closest to
Part 3
The seasonal index for Saturday is closest to
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Using the appropriate seasonal index in Table 2, determine the deseasonalised value for the summer rainfall in 2008. Write your answer correct to the nearest millimetre. (1 mark)
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The following information relates to Parts 1, 2 and 3.
The table shows the seasonal indices for the monthly unemployment numbers for workers in a regional town.
Part 1
The seasonal index for October is missing from the table.
The value of the missing seasonal index for October is
A.
B.
C.
D.
E.
Part 2
The actual number of unemployed in the regional town in September is 330.
The deseasonalised number of unemployed in September is closest to
A.
B.
C.
D.
E.
Part 3
A trend line that can be used to forecast the deseasonalised number of unemployed workers in the regional town for the first nine months of the year is given by
deseasonalised number of unemployed = 373.3 – 3.38 × month number
where month 1 is January, month 2 is February, and so on.
The actual number of unemployed for June is predicted to be closest to
A.
B.
C.
D.
E.
The following information relates to Parts 1, 2 and 3.
The time series plot below shows the revenue from sales (in dollars) each month made by a Queensland souvenir shop over a three-year period.
Part 1
This time series plot indicates that, over the three-year period, revenue from sales each month showed
A. no overall trend.
B. no correlation.
C. positive skew.
D. an increasing trend only.
E. an increasing trend with seasonal variation.
Part 2
A three median trend line is fitted to this data.
Its slope (in dollars per month) is closest to
A.
B.
C.
D.
E.
Part 3
The revenue from sales (in dollars) each month for the first year of the three-year period is shown below.
If this information is used to determine the seasonal index for each month, the seasonal index for September will be closest to
A.
B.
C.
D.
E.
The seasonal indices for the first 11 months of the year, for sales in a sporting equipment store, are shown in the table below.
Part 1
The seasonal index for December is
A.
B.
C.
D.
E.
Part 2
In May, the store sold $213 956 worth of sporting equipment.
The deseasonalised value of these sales was closest to
A.
B.
C.
D.
E.
Use the following information to answer Parts 1 and 2.
The table below shows the long-term average rainfall (in mm) for summer, autumn, winter and spring. Also shown are the seasonal indices for summer and autumn. The seasonal indices for winter and spring are missing.
Part 1
The seasonal index for spring is closest to
A.
B.
C.
D.
E.
Part 2
In 2011, the rainfall in autumn was 48.9 mm.
The deseasonalised rainfall (in mm) for autumn is closest to
A.
B.
C.
D.
E.
