SCSA Mathematics Applications Time series analysis
5 sample questions with marking guides and sample answers · Avg. score: 51.6%
The table shows the maximum daily temperature (°C) for a week.
| Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|---|---|---|---|---|---|
| 24.4 | 25.2 | 24.6 | 25.2 | 25.6 | 25.7 | 25.9 |
If the simple 5-point moving average for Wednesday is 25.0 °C, what is the simple 5-point moving average (°C) for Friday?
25.4
25.5
25.6
26.0
The table shows time series data for a company's quarterly sales.
| Quarter | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Sales ($) | 2700 | 3600 | 4500 | 7200 |
| Seasonal index | 0.6 | 0.8 | 1.0 | — |
Determine the seasonally adjusted sales ($) for the fourth quarter.
4500
6000
8640
11 520
The table shows Darwin’s actual rainfall (mm) each season for two years.
| 2022 | 2023 | |
|---|---|---|
| Autumn | 410 | 390 |
| Winter | 30 | 20 |
| Spring | 205 | 150 |
| Summer | 1135 | 1100 |
Calculate the seasonal index for each season in Darwin.
This table shows Hobart’s actual rainfall (mm) each season for 2023 and the long-term seasonal indices.
| Autumn | Winter | Spring | Summer | |
|---|---|---|---|---|
| 2023 rainfall (mm) | 130 | 145 | 155 | 132 |
| Seasonal index | 0.92 | 1.02 | 1.12 | 0.94 |
Deseasonalise the Hobart rainfall data to identify the 2023 season with the highest seasonally adjusted rainfall.
Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years.
| Autumn | Winter | Spring | Summer | |
|---|---|---|---|---|
| 2021 | 285 | 28 | 195 | 460 |
| 2022 | 276 | 22 | 170 | 392 |
Deseasonalise the data.
The table shows the profit made each year (in thousands of dollars) by a small business.
| Year | Profit ($'000s) |
|---|---|
| 2015 | 42.1 |
| 2016 | 36.9 |
| 2017 | 48.4 |
| 2018 | 52.3 |
| 2019 | 56.1 |
| 2020 | 59.8 |
Use a mathematical model to determine the equation of the least-squares line to fit this data.
Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.