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Chapter 2   Basic graphical displays

2.1   Density and histograms

2.1.1   Histogram as a display of density

Histograms show a distribution of marks without identifying individual values. They contain less visual 'noise', especially for large data sets.

2.1.2   Choice of classes

Histogram class widths should be adjusted to give the smoothest possible outline.

2.1.3   Relative frequency and area

In a histogram, the area above any part of the axis is equal to the proportion of data values in that region.

2.1.4   More about histogram bin width

Histograms bins usually all have the same width. However the effect of combining two bins or splitting a bin helps explain the fundamental relationship between histogram area and proportion.

2.1.5   Frequency polygolons

Joining the tops of adjacent histograms gives a frequency polygon.

2.1.6   Drawing histograms

A histogram is usually drawn from a frequency table. Histograms can be drawn in Excel, but not easily.

2.2   Normal distributions

2.2.1   Smoothing a histogram

The histograms of large data sets tend to be fairly smooth. A smooth curve called a probability density function may be used to summarise it.

2.2.2   Normal distributions

One particular class of curves called the family of normal distributions is often used as a 'model' for mark data. Two 'parameters' can be adjusted to match the curve to actual data.

2.2.3   Normal probabilities

Normal distribution curves have similar properties to histograms. In particular, the proportion of values in any range equals the area under the curve.

2.3   Discrete and categorical data

2.3.1   Discrete and continuous data

Mark data are usually counts and are therefore discrete.

2.3.2   Bar charts

If discrete data cover a large range of counts, a histogram can be used. If there are only a small number of possible values, a bar chart is better.

2.3.3   Categorical data

Some assessment information is categorical rather than numerical. Bar charts can also be used to display categorical data.

2.3.4   Stacked bar charts and pie charts

These are alternative displays of discrete and categorical data.

2.3.5   Drawing bar and pie charts

Information is given about drawing bar and pie charts in Excel.