Describe the whole series
Read time horizontally and response vertically. Describe direction, variation and unusual observations with values and times, then state the limits of the evidence
- Trend Use the full interval. A short reversal does not necessarily change the overall direction
- Isolated departure A value that departs and is followed by a return is a possible outlier relative to nearby observations
- Persistent change Several later observations staying at a new level are different from one isolated point
- Interpretation A graph can suggest explanations; verify records and context before correcting data or making causal claims
Worked example
The six daily observations are 20, 22, 60, 21, 23 and 22 kL. Describe the unusual feature and one limitation
- \(\displaystyle 60-22=38\)Day 3 is 38 kL above day 2 and much higher than its neighbours
- \(\displaystyle 21,23,22\)Days 4 to 6 return near the earlier level, supporting an isolated unusual observation rather than a sustained increase
- \(\displaystyle \text{Check the source}\)The plot does not establish whether the high value is genuine, a copying error or an instrument problem
Common mistakes
Difficulty levels
Questions about this topic
Does an outlier have to be a mistake?+
No. It may represent a genuine unusual event. Check the source and context before correcting or excluding it
Can a decreasing trend contain an increase?+
Yes. Trend describes the overall interval; short movements can go the other way
Is the neighbour comparison a formal outlier rule?+
No. Here it helps describe an isolated departure. Formal numerical rules require an explicitly chosen method and may not suit a trending series
Can one peak prove seasonality?+
No. Repetition at matching calendar positions must be observed across more than one cycle
Does a time pattern establish its cause?+
No. Check contextual evidence and alternative explanations. Coinciding events alone do not establish causation
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics