Fortunately, this is where things get a bit easier as the mode and range are particularly simple statistical measures to understand.

Take the following set of results for an S4 class’ National 5 Maths prelim:

Let’s establish a few definitions:

Having the dataset laid out in a simple, numerically ordered line can make things easier:

25\%, 35\%, 48\%, 51\%, 60\%, 60\%, 67\%, 76\%, 83\%, 95\%

Clearly there is only one result which appears more than once – 60% appears twice. Therefore, 60% is the mode of this dataset. It’s that simple.

Calculating the range requires first knowing the maximum and minimum values of the dataset. As we have already rearranged the dataset into numerical order, these are easy to establish:

25\%, 35\%, 48\%, 51\%, 60\%, 60\%, 67\%, 76\%, 83\%, 95\%

\begin{aligned}&Maximum=95\% \\[12pt]&Minimum=25\% \\[12pt]&Range=Maximum-Minimum \\[12pt]&Range=95\%-25\% \\[12pt]&Range=70\%\end{aligned}

The range of the dataset is 70%. This means that the data is spread over an interval of 70% – think of the dataset as having a “width” of 70%. All other results fall within the 70% interval defined by the minimum (25%) and maximum (95%) results:

As a final point of interest, notice that if no value appears more frequently than the other values in a dataset, then by definition, the dataset must have no mode. This is a quality which differentiates the mode from the other statistical terms we have learned in this module – all datasets have a mean, median and range, but it is possible for a dataset to have no mode!