- 1. Consolidating the Averages in Real Contexts
Find the mean, median, mode and range of ungrouped data, choose the summary that answers a real question, and write a justified conclusion.
- 2. Two Variables at Once: Bivariate Data
Define bivariate data as two measurements for the same item, decide whether two variables rise together, move oppositely or are unrelated, and recognise the limitation of a relationship.
- 3. Plotting a Scatter Graph
Plot bivariate data on a scatter graph with variable 1 on the horizontal axis and variable 2 on the vertical axis, read values off the graph, and draw one from a table with sensible scales.
- 4. Describing Correlation
Read the shape of a scatter cloud to describe its correlation as positive, negative or none, judge its strength as strong or weak, and match a described relationship to the correct type.
- 5. Outliers on a Scatter Graph
Identify an outlier on a scatter graph as a point far from the overall pattern, suggest a sensible real-world reason for it, and ignore it when judging the overall correlation.
- 6. Correlation Is Not Causation
Understand that a correlation does not prove causation; identify a likely cause, a hidden third variable, or a coincidence; and plot the causal variable on the horizontal axis.
- 7. The Line of Best Fit
Draw a sensible line of best fit that follows the trend and passes through the middle of the points, understand it is one straight line and not a dot-to-dot, and improve accuracy by passing it through the mean point.
- 8. Predicting: Interpolation and Extrapolation
Use a line of best fit to predict an unknown value, tell interpolation (within the data) from extrapolation (beyond the data), and judge honestly how reliable each prediction is.
- 9. Time Series Graphs and Seasonal Variation
Construct and interpret a time series graph, describe its trend and any seasonal variation, and explain why a single figure from a time series can mislead.
- 10. Moving Averages: Smoothing the Seasons
Calculate a four-point moving average by averaging successive groups of values, slide the group along the series, and use the smoothed values to reveal the underlying trend hidden beneath seasonal variation.
- 11. A Full Relationships-and-Trends Enquiry
Run a complete bivariate enquiry — plot a scatter, describe the correlation, check outliers and causation, fit a line of best fit through the mean point and predict with a reliability judgement — and read a time series for its trend and seasonal variation, smoothing with a moving average.
