01 · Coordinates
A trial records 7 cm and 42 lux. With distance horizontal, give the plotted coordinate.
Hint
Use horizontal variable first.
Worked solution
(7,42). The units belong on the labelled axes.
Understand · explore · practise
Scatter diagrams and paired data
Keep paired observations together, choose explanatory and response axes, plot labelled scatter diagrams and handle repeated or missing pairs honestly.
Before you startCoordinates, units and numerical data.
01 / Keep each pair together
One observation supplies both coordinates.
A scatter point is (x,y) from the same case.
Sorting the two columns separately destroys the pairing.
A scatter diagram displays how two numerical variables vary together. In the fictional lamp data, each distance and light reading belong to the same trial. Plot all pairs before describing any pattern.
Find the paired observationExplore
Fictional lamp experiment: distances in cm are 10, 15, 20, 20, 25, 30; corresponding light readings in lux are 80, 52, 35, 35, 24, 18.
Observation 1 pairs distance 10 cm with light reading 80 lux. Six observations occupy five distinct positions because two pairs coincide.
02 / Read rows as observations
The pairing carries information.
Three fictional journeys have (distance in km, time in minutes): (2,14), (5,12), (8,25).Worked example
Plot (2,14), (5,12), (8,25)
A shorter journey need not take less time in every case.
Separately sorting would produce (2,12), (5,14), (8,25)
Those are different data.
Keep each row intact when sorting or filtering
Use a case identifier when joining tables.
02 · Broken pairing
Two original pairs are (1,9) and (3,4). A student plots (1,4) and (3,9). Has the dataset been preserved?
Hint
Each original row must remain intact.
Worked solution
No. Both marginal lists are unchanged, but the association has been reversed by exchanging the responses.
03 / Choose the prediction direction
Explanatory does not automatically mean causal.
Put the explanatory variable on the horizontal x-axis and the response on the vertical y-axis.
State the purpose if either direction could be of interest.
If the task is to predict light reading from distance, distance is explanatory and light reading is the response. For two observational measurements with no specified prediction direction, explain your axis choice. Calling one variable explanatory does not establish that it causes the other.
03 · Prediction purpose
A model predicts delivery time from journey distance. Which variable goes on each axis?
Hint
The supplied predictor is x.
Worked solution
Distance on x; delivery time on y, with units on both.
04 · Causal label
A scatterplot puts hours of revision on x and scores on y. Does the axis choice prove revision caused the differences?
Hint
A plotting decision is not a study design.
Worked solution
No. Prior attainment, selection and other factors may also matter. The diagram alone does not establish causation.
04 / Locate a point in two directions
Across for x, then up for y.
Watch: one row becomes one point
Pause, replay or seek freely. The notes explain the same idea and stay in view.
Plot the fictional pair (15 cm,52 lux).Worked example
Locate 15 on the distance axis
Check the tick spacing and units.
Move vertically to height 52 lux
Do not exchange x and y.
Mark one point at that intersection
Guide lines help placement; they are not a fitted model.
05 · Scale reading
Horizontal ticks 0,10,20 are equally spaced. Where does x = 15 lie?
Hint
Use a linear scale.
Worked solution
Halfway between 10 and 20. The same spacing must represent the same numerical change.
06 · Origin
Must every scatterplot axis start at zero?
Hint
Unlike histogram area, scatter coordinates do not encode count through rectangle area.
Worked solution
No. A restricted labelled linear range can show the data clearly. Make the scale explicit and avoid using apparent steepness alone to judge association strength.
05 / Show repeated observations
A plotted position is not necessarily one case.
07 · Identical pairs
Six recorded pairs include (20,35) twice. How many distinct plotted positions can the six pairs occupy if all others differ?
Hint
The duplicate points coincide.
Worked solution
Five positions, representing six observations. A count label or another transparent overlap convention can reveal multiplicity.
08 · Same x, different y
Are pairs (20,35) and (20,38) invalid because x repeats?
Hint
Several cases may share the same explanatory value.
Worked solution
No. Plot both vertically above x = 20 at their respective y values. A scatter diagram need not be the graph of a single-valued function.
06 / Keep missingness visible in the record
Do not invent a coordinate.
09 · Missing response
A row has x = 25 but y is missing. Where should its scatter point go?
Hint
A point needs both coordinates.
Worked solution
It cannot be plotted as an observed pair. Record the missing response and state the number of complete pairs. Do not substitute zero without evidence.
10 · Predicted value
A model predicts a missing y as 24. May it be added indistinguishably to the observed scatter points?
Hint
An estimate is not a measurement.
Worked solution
No. Keep it labelled and visually distinct if shown. Do not silently treat it as an independent observed pair when assessing the same model.
07 / Inspect before drawing a line
Points come before a summary model.
11 · Joining points
Should all scatter points automatically be joined in the order of the table rows?
Hint
Row order may be arbitrary.
Worked solution
No. A scatter diagram shows pairs. Joining arbitrary rows can suggest a path that has no meaning. Use a separately justified fitted trend if required.
12 · A curved pattern
Light readings decline as distance increases, but the points follow a curve. Is a straight-line fit automatically appropriate?
Hint
Direction and shape are separate features.
Worked solution
No. Describe the decreasing association and curved shape. A straight-line model needs a suitability check and may only approximate a limited range.
08 / Audit the data and the display
Pairing, axes, units, scale and completeness.
Retain rows, plot each complete pair and label both axes with units. Reveal overlapping observations and keep missing or predicted values distinct. Describe the pattern before choosing any fitted model.
Section 1 of 8 · Keep each pair together