Construct a scatterplot
Keep each numerical pair together and plot one point per case. Coincident cases may share a visible marker
\[(x,y)\]
- Axes Use the explanatory variable horizontally and the response vertically, with units
- Scale Use uniform numerical spacing on each axis and include all observations. The axes need not start at zero
- Pairs Table orientation and row order do not change which values belong together
- No invented sequence Do not connect distinct cases in arbitrary table order
Worked example
A maker predicts mass from length. A row records mass 28 g and length 5 cm. State where to plot it and why
\[(x,y)=(5,28)\]
- \(\displaystyle x=5\)Length is the explanatory measurement, regardless of table order
- \(\displaystyle y=28\)Mass is the response for that same sample
- \(\displaystyle (5,28)\)Move horizontally to 5 cm, then vertically to 28 g
Common mistakes
Swapped pair
✕\(\displaystyle (28,5)\)✓\(\displaystyle (5,28)\)
Length is horizontal and mass vertical in this investigationCounting markers without checking overlap
✕\(\displaystyle 4\text{ markers}=4\text{ cases always}\)✓\(\displaystyle \text{check coincident cases}\)
Several recorded observations can occupy one coordinateDifficulty levels
introIdentify the axes, read a paired case and choose a plot containing every observation
standardHandle the response variable listed first, cropped axes and exchanged-axis candidates
challengePlot a duplicate-free ten-case table with close cases and distinguish an omitted point
examChoose the scatterplot that matches the table's axes and every paired point
Questions about this topic
Must both axes start at zero?+
No. Clearly labelled restricted scales may be used. Include every observation and do not let a cropped scale hide data
Should I connect scatterplot points?+
No, not in arbitrary table order. A fitted trend is a separate summary; it is not a join-the-dots sequence
What if two cases have identical coordinates?+
Plot both at that coordinate and make the multiplicity clear when it matters. Do not quietly change their values
Can the table list the response first?+
Yes. Use the investigation question to assign axes and read each paired case correctly
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