Long page
descriptions

Chapter 1   Looking at marks

1.1   Displaying individual marks

1.1.1   Dot plots

A dot plot displays each value as a cross along a numerical axis. Dot plots can be jittered or stacked to help distinguish individual crosses.

1.1.2   Stem and leaf plots

Stem and leaf plots are similar to stacked dot plots, but hold more information.

1.1.3   Splitting the stems

For some data sets, a basic stem and leaf plot gives too coarse a grouping of values. This page describes a simple modification that gives more flexibility in the display.

1.1.4   Creating the plots

Dot plots can be drawn (with a little effort) in Excel. Stem and leaf plots cannot be produced in Excel but are easy to draw by hand.

1.2   What does a distribution show?

1.2.1   Outliers

An extreme mark should be carefully examined. Was there an error?

1.2.2   Clusters

Sometimes the marks are clustered into groups. Do these clusters correspond to any other characteristics of the students?

1.2.3   Centre, spread and shape

Graphical displays show a 'typical' mark (centre of the distribution) and the variability of the marks (the spread of the distribution). A long tail to the distribution may also be visible (skewness).

1.2.4   Displaying extra information

Statistical software can dynamically show student names or other information. Annotating a printed display is an alternative.

1.2.5   Danger of overinterpretation

Class marks are usually small data sets (around 30 values). Features may appear by chance without any meaningful underlying cause.