Construct and read a time plot
Time is horizontal and the recorded response is vertical. Keep each observation paired with its own time and retain the units
\[(t,y_t)\]
- Order Sort complete time–response pairs chronologically before connecting them
- Scales Use equal numerical steps and proportional time gaps. Include every observation in the plotting window
- Signed change Subtract the earlier response from the later response \(\displaystyle \Delta y=y_{\text{later}}-y_{\text{earlier}}\)
- Percentage points Subtracting two percentage levels gives a percentage-point change, not a relative percentage change
Worked example
A table lists day 4: 38 kL, day 1: 20 kL, day 3: 42 kL and day 2: 35 kL. Give the plotting order and the change from day 2 to day 4.
\[x=\text{day},\quad y=\text{kL}\]
- \(\displaystyle (1,20),\ (2,35)\)Start with days 1 and 2, keeping their responses attached
- \(\displaystyle (3,42),\ (4,38)\)Then plot days 3 and 4 and connect consecutive days
- \(\displaystyle \Delta y=38-35=3\)The day 2 to day 4 change is +3 kL over two days
Common mistakes
Reversing coordinates
✕\(\displaystyle (42,3)\)✓\(\displaystyle (3,42)\)
Day 3 with response 42 is time first, response secondDropping the sign
✕\(\displaystyle 38-42=4\)✓\(\displaystyle 38-42=-4\)
Later minus earlier is negative for a decreaseConfusing percentage measures
✕\(\displaystyle 55\%-40\%=15\%\text{ increase}\)✓\(\displaystyle 55-40=15\text{ points}\)
The percentage-point change is 15; the relative increase is 37.5% because 15 is 37.5% of 40.Difficulty levels
introChronological observations are used to select a correct plot and read one response value
standardNamed periods and table layouts are combined with a response or period-index read
challengeShuffled observations must be ordered before a change between two periods is calculated
examA compact plot-selection choice tests axes, joins and chronological order together
Questions about this topic
Must a time plot start its vertical axis at zero?+
Not always. A clearly labelled restricted scale can help show variation, but it changes visual steepness. Report actual values and avoid misleading comparisons
Should I sort the response values?+
No. Sort the times and retain the response belonging to each time. Sorting responses separately fabricates a different series
What if a time is missing?+
Preserve the actual elapsed-time gap and identify the missing observation. Do not silently invent a measured value
What does a line between points mean?+
It connects the recorded sequence. Reading between points uses an interpolation assumption
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics
In this chapter
Classify data types5A Data collection and types: Collect data and evaluate biasBuild a frequency and percentage frequency tableBuild a bar chart from a frequency tableGroup numerical data into class intervalsConstruct a histogram from a frequency tableRead values from a histogramDescribe the shape of a distributionChoose an appropriate display for a variableRead values from a frequency table or bar chart5B Frequency tables and histograms: Critique statistical displays and claimsConstruct a dot plot from raw dataConstruct an ordered stem plot from raw data5C Dot plots and stem-and-leaf plots: Compare a numerical variable across groupsMean, mode, median and range of a data listFind the mean and the median, and choose between themFind measures of centre from a frequency displayFind the range, the quartiles and the IQRFind the fences and identify outliers5E Quartiles, interquartile range and outliers: Produce a five-number summary and construct a boxplot5F Box plots: Produce a five-number summary and construct a boxplotRead values and percentages from a boxplot5F Box plots: Compare a numerical variable across groupsPlot, read and classify a basic time-series graphConstruct and read a time series plotIdentify qualitative features in a time seriesIdentify the explanatory and response variablesConstruct a scatterplot from a data tableRead a scatterplotDescribe an association from a scatterplotAssociation is not causationFit a line of best fit by eye and make estimatesCompare categorical groups using two-way tables