Tables, Charts, and Graphs

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infoWhy this? Scatter graphs reveal relationships between numerical variables, while pie charts communicate proportions within a whole. Interpreting correlation, outliers, predictions, and sectors develops statistical judgement as well as accurate representation.

scheduleWhy now? This unit builds on Year 7 charts, line graphs, coordinates, and percentages. It introduces bivariate data and proportional sectors before later work on more formal prediction, conversion graphs, and grouped representations.

A scatter graph shows the relationship between two numerical variables by plotting ordered pairs `(x, y)` as points on perpendicular axes.
In a scatter graph, the independent variable is usually placed on the horizontal axis (x-axis) and the dependent variable on the vertical axis (y-axis).
A scatter graph needs a title and both axes labelled with the variable name and units (if given) so the data can be interpreted correctly.
Positive correlation means that, as one variable increases, the other variable tends to increase, so the points trend upwards from left to right.
Negative correlation means that, as one variable increases, the other variable tends to decrease, so the points trend downwards from left to right.
No correlation means there is no clear trend in the points, so knowing one variable does not help to predict the other.
Correlation describes a pattern in data but does not prove that one variable causes the other (correlation is not causation).
The strength of correlation depends on how closely the points cluster around a trend; closer to a line means stronger correlation.
An outlier is a point that does not fit the overall pattern of the data and may be an error or an unusual value.
A line of best fit is a straight line drawn on a scatter graph to summarise the overall trend and help make predictions.
Predictions from a line of best fit are estimates, and they are less reliable if they involve values outside the range of the given data (extrapolation).
A pie chart represents categorical data as sectors of a circle, where each sector shows a proportion of the whole.
A full pie chart is a complete circle, and the total of all sector angles is `360^\circ`.
The angle for a pie chart sector can be found using `\text{angle} = \frac{\text{category frequency}}{\text{total frequency}} \times 360^\circ`.
In a pie chart, larger frequencies (or proportions) correspond to larger sector angles, and the sectors should be labelled clearly (category names and/or values).

rocket_launchYou must be able to

Choose an appropriate scale and label axes, then plot points accurately on a scatter graph using the correct `x` and `y` values.
Describe correlation from a scatter graph by stating the direction (positive/negative/none) and commenting on strength using the clustering of points.
Identify outliers on a scatter graph by comparing points to the overall trend, and state how an outlier could affect conclusions or a line of best fit.
Draw a line of best fit by eye so that there are roughly equal numbers of points above and below it, following the general trend (do not force it through all points).
Use a line of best fit to estimate one variable from the other by reading across to the line and then down/up to the relevant axis, and state that the answer is an estimate.
Convert a frequency table into pie chart angles using `\frac{\text{frequency}}{\text{total}} \times 360^\circ`, rounding sensibly so angles sum to `360^\circ`.
Construct a pie chart with a protractor by drawing a circle, marking sector angles from a start line, drawing radii for each sector, and adding clear labels or a key.

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