Interpreting data from Scatter plot - TARSOG

Read and quantify data directly off a bivariate scatter plot, then use the TARSOG framework (Trend, Association, Relationship, Scatter, Outliers, Grouping) to describe what it shows -- including naming the explanatory/response variable, using the line of best fit to predict a value, and judging whether that prediction is interpolation or extrapolation. Distinct from the existing lo-analysing-scatter-plots-i-e-bivariate-tarsog, which mixes verbal TARSOG-vocabulary recall with some diagram reads; this LO's task decks embed a live \PicStatisticsScatter diagram in every card and always require a numeric prediction, an outlier's quantified gap from the trend, or an explanatory/response judgement, not just a TARSOG label.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • S6-1
  • S5-1
New NZC (2026)
  • NZC26-P4-STA-VIS-K-Y9-03
  • NZC26-P4-STA-VIS-P-Y10-01
  • NZC26-P4-STA-VIS-K-Y9-01
  • NZC26-P4-STA-INT-K-Y10-02
  • NZC26-P4-STA-INT-P-Y10-03
  • NZC26-P4-STA-INT-K-Y10-03

Resources

  • Beta: Scatter plot - TARSOG Skills in Ex 31.01, pg 579
  • CorbettMaths worksheet on Scatter GraphsQuestions PDF · Answers

Terminology

  • Bivariate Data
  • Line of Best Fit (Trend line)
  • Trend (Linear vs. Non-linear)
  • Association (Positive vs. Negative)
  • Relationship (Strong, Moderate, Weak)
  • Scatter (Constant vs. Fanning)
  • Outliers (Unusual points)
  • Grouping (Clusters)
  • Explanatory (independent) vs response (dependent) variable
  • Interpolation vs extrapolation

Task goals

  • Identify the explanatory (independent) and response (dependent) variable in a scatter plot's context.
  • Describe the trend (linear/non-linear) and association (positive/negative) shown by the main cluster of points.
  • Judge the strength of the relationship (weak/moderate/strong) from how closely points cluster around the line of best fit.
  • Identify an outlier's coordinates and calculate how far its actual value departs from what the line of best fit predicts at that x-value.
  • Use the line of best fit to predict a value, and correctly classify the prediction as interpolation (within the data range) or extrapolation (beyond it), explaining why extrapolated predictions are less reliable.
  • Recognise when two distinct groupings exist in one scatter plot (via a key), and explain why a single combined line of best fit would be misleading.

Where this fits

What leads into this objective, and where it goes next.

Before

Selecting appropriate displays

Selecting appropriate displays

Interpreting data from Time series - TSN

Interpreting data from Time series - TSN

Interpreting data from box and whisker - CSSI

Interpreting data from box and whisker - CSSI

You are here

Interpreting data from Scatter plot - TARSOG

Interpreting data from Scatter plot - TARSOG

Know

In relationship investigations: sometimes one variable is thought of as predictive of the other variable; then the response or dependent variable is on the y-axis, and the 'predictive', explanatory, or independent variable is on the x-axis; an eyeballed line or curve of best fit can be added for paired numerical data.

Statement▸
Year 9 · Statistics · Visualisation of data
NZC26-P4-STA-VIS-K-Y9-03
Know

A distribution is formed from all the possible values of a variable and their frequencies. It can be shown using data visualisations that show patterns, trends, and variations and that include dot plots, bar graphs, frequency tables, box plots, histograms, time-series graphs, scatter plots, and two-way tables.

Statement▸
Year 9 · Statistics · Visualisation of data
NZC26-P4-STA-VIS-K-Y9-01

Next

Analysing scatter plots (i.e. bivariate) - TARSOG

Analysing scatter plots (i.e. bivariate) - TARSOG

Selecting appropriate displays

Selecting appropriate displays

Also under S6-1:

Also under S5-1:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.