Read the data, labels and scale
Read horizontally first and vertically second. State the units and distinguish an observed value from an estimate
\[(x,y)\]
- Extremes Farthest right means greatest x. Highest means greatest y. These need not be the same case
- Scaled units A reading of 4 on an axis in hundreds represents 400 actual units
- Count carefully Distinct markers equal cases only when no observations coincide. Otherwise check multiplicities or the source table
- Missing observations A location between recorded points is not itself a measured case
Worked example
The case with the highest response lies at (4,60). The horizontal axis is distance in hundreds of kilometres and the vertical axis is fuel used in litres. Give the actual pair
\[(x,y)=(4,60)\]
- \(\displaystyle 4\times100=400\)Convert the horizontal reading to kilometres
- \(\displaystyle y=60\)The vertical axis already measures litres
- \(\displaystyle (400,60)\)Report kilometres first, litres second. Highest response does not mean farthest right
Common mistakes
Ignoring units
✕\(\displaystyle 4\text{ hundred}=4\)✓\(\displaystyle 4\times100=400\)
The unit multiplier is part of the axis labelDistinct markers always equal cases
✕\(\displaystyle \text{markers}=\text{cases always}\)✓\(\displaystyle \text{check overlaps}\)
Two or more observations can have exactly the same pair of valuesWrong extreme
✕\(\displaystyle \text{highest}=\text{greatest }x\)✓\(\displaystyle \text{rightmost}=\text{greatest }x\)
Height measures the vertical responseDifficulty levels
introRead the explanatory and response axes, count the points and locate the point with the largest explanatory value
standardRead a point with an extreme response value on a scatterplot whose axes may start above zero
challengeRead an extreme point from a 12-point scatterplot and convert a coordinate on a scaled axis
examChoose the coordinate pair that keeps the axis order, extreme point and scale correct
Questions about this topic
How many cases does a scatterplot show?+
Count the observations, including multiplicities. Distinct visible markers equal cases only if no points overlap
Which coordinate comes first?+
The horizontal coordinate comes first, with its stated units or scale conversion, then the vertical coordinate
Can I read an unrecorded value between points?+
Only as an estimate under a stated model or assumption. Do not call it a measured observation
Can two cases share a horizontal coordinate?+
Yes. Their vertical responses may be different; only identical pairs coincide completely
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
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