VCAA General Mathematics Data analysis, probability and statistics
5 sample questions with marking guides and sample answers
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
A sample of university staff and students was asked whether they preferred catching public transport or driving their own car to university. The data collected is shown in the table.
| Public transport | Drive own car | |
|---|---|---|
| Staff | 2 | 18 |
| Students | 48 | 12 |
What percentage of university students prefer to drive their own car?
12%
15%
20%
40%
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.
Each of the 60 performers in a music and dance concert is either a Year 11 or Year 12 student and either a musician or a dancer.
There are four more Year 11 students than Year 12 students. One quarter of the Year 11 students are dancers and half of the Year 12 students are dancers.
Complete the two-way frequency table to calculate the percentage of students who are musicians.
| Year 11 | Year 12 | Total | |
|---|---|---|---|
| Musician | |||
| Dancer | |||
| Total | 60 |
Data was collected relating the number of hours spent fishing and the total number of fish caught.
The linear model for this data was found to be , where is the number of hours spent fishing, and is the total number of fish caught.
Use the model to predict the number of fish caught if 12 hours were spent fishing.
The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid.