These notes recap Topic 4.2. For worked examples, read the study guide.
Recap
- A data set is a collection of specific pieces of information.
- Data sets can be manipulated and analysed to solve a problem or answer a question.
- Values are accessed and used one at a time and then processed to give the desired outcome.
- Data can be represented in a chart or table, which can be used to plan the algorithm.
- Patterns and algorithms can be described in written language or diagrams (such as a flowchart).
Key relationships
| Plan step | What it does | Example (rainfall data) |
|---|---|---|
| Set up | Create what must be remembered | wetDays = 0, or best = first position |
| Repeat for each value | Examine one value, update what is remembered | If reading >= 10, add 1 |
| Report | Give the answer after all values | Report wetDays |
Standard plans in outline
| Task | Remember | Update rule |
|---|---|---|
| Count with a property | A count (0 at start) | Add 1 when the property holds |
| Total | A running total (0 at start) | Add each value |
| Largest | Best so far (start from the first value) | Replace it when a value is larger |
| Average | Total and number of values | Total divided by number of values at the end |
Worked reminder
Rainfall on seven days is 0, 12, 5, 20, 0, 8, 15 mm. The count of days with at least 10 mm is 3 (Tue, Thu, Sun). The largest is 20 mm on Thursday. The total is 60 mm and the mean is 60 ÷ 7, about 8.57 mm. A plan that resets the count to 0 inside the loop reports only whether the last reading qualifies, so it gives 1 instead of 3.
Checking a plan
- Choose a data set small enough to trace by hand, with an answer you can see by eye.
- Write one table row per value and one column per remembered quantity.
- Compare the final row with the answer you expected.
- If they differ, look first at where each remembered quantity is set up and where it is updated.
Mistakes to avoid
- Putting a set-up step (a count or total starting at 0) inside the repeated part.
- Starting a maximum at 0 for data that can be negative.
- Forgetting to say what is reported at the end.
- Treating the data set and the Java array as the same thing.
- Skipping the trace table.
Quick self-check
- What are the three parts of most plans for a data set? Answer: set up, repeat for each value, report.
- For the data 3, 8, 2, 9, 4, how many values are below 5? Answer: 3 (the values 3, 2 and 4).
- Why should a maximum start from the first value? Answer: starting from 0 fails if all values are negative; the first value is always a valid starting candidate.
- Name a way to represent an algorithm other than code. Answer: a flowchart, a table or written steps.