S-Cool Revision Summary

S-Cool Revision Summary

Stem-and-leaf and box-and-whisker diagrams

A stem-and-leaf diagram is one way of taking raw data and presenting it in an easy and quick way to help spot patterns in the spread of the data. They are best used when we have a relatively small set of data and want to find the median or quartiles.

A box-and whisker diagram is a basic diagram used to highlight the quartiles and median to give a quick and clear way of presenting the spread of the data.

There are 5 points to remember when drawing a box-and-whisker diagram. They are:

Stems, Leaves, Boxes and Whiskers


Values of data are usually labelled as outliers if they are more than 1.5 times of the inter-quartile range from either quartile.

Shapes of distributions

Symmetrical distribution: The median is in the middle exactly halfway from each quartile. This is what we would class as a normal distribution.

Symmetrical distribution

Negatively skewed distribution: there is a greater proportion of the data at the upper end.

Negatively skewed distribution

Positively skewed distribution: there is a greater proportion of the data at the lower end.

Positively skewed distribution


Histograms are best used for large sets of data, especially when the data has been grouped into classes. They look a little similar to bar charts or frequency diagrams, but in histograms the frequency of the data is shown by the area of the bars and not just the height. They are most commonly used for continuous data.

The vertical axis of a histogram is labelled 'Frequency Density' and is calculated by the following formula:

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Cumulative frequency

Cumulative frequency is kind of like a running total. We add each frequency to the ones before to get an 'at least' total. Best to use if we need knowledge of the median and quartiles.

These cumulative frequencies ('at least' totals) are plotted against the upper class boundaries to give us a cumulative frequency curve.