Scatter Graphs

Activities to try

1. 1

   Plot and balance a line of best fit

   Why it works: The line of best fit is one straight summary of the whole point cloud, positioned so points balance either side - it is not a path connecting consecutive points and is not required to pass through the origin.

   1. Take a table of paired measurements (e.g. 10 pupils' height and arm-span) and plot each pair as one cross on a two-axis grid.
   2. Label both axes with the variable names and choose a consistent, linear scale; where the data does not start near zero, use an axis break rather than distorting the scale.
   3. First judge the direction of the correlation from the overall pattern (if there is no correlation, do not draw a line). Then draw a SINGLE straight trend line in that direction and adjust it (tilt and shift) until roughly equal numbers of points sit above and below along its whole length.
   4. Deliberately draw a wrong dot-to-dot zig-zag joining consecutive points alongside the correct line, and explain in words why the single trend line, not the join, summarises the whole cloud.
   5. State the correlation type (positive, negative, or none) from the overall pattern.
2. 2

   Interpolate inside, question outside

   Why it works: Estimating within the observed data range is reasonable (especially with a strong correlation), but extending the line beyond the data gives an unreliable prediction because the trend may not continue.

   1. On a scatter with a correct line of best fit, mark the data range on the x-axis (the lowest to highest observed value).
   2. Read off an estimated y-value for an x inside the range (e.g. predicted score for 5 hours' revision when the data runs 1-8 hours), and state it as a reasonable estimate.
   3. Attempt a prediction well beyond the data (e.g. 20 hours) and explain why that value is unreliable because the trend is not known to continue.
   4. Note that interpolated estimates are more trustworthy when the correlation is strong, and keep every read-off tied to its context so the number means something.
3. 3

   Check reading and choice (scorable practice)

   Why it works: Being able to recognise a good line and read inside the range confirms understanding, but it does not by itself demonstrate the ability to construct and balance a line from raw data.

   1. Given a scatter with a line already drawn, describe the correlation and read an interpolated value.
   2. Choose the correct line of best fit from options that include a dot-to-dot join, an unbalanced line, and a well-balanced line, and justify the choice.
   3. Decide whether a far-outside prediction is reliable and explain why not.
   4. Place a line of best fit onto a given scatter (accepting a small range of acceptable positions).