Mode & Range

Use our extensive free resources below to learn about Mode & Range.

This material is an extract from our National 5 Mathematics: Curriculum Breakdown course led by instructor Andrew Eadie. Enrol in the full course now and gain access to over 100 detailed topic breakdowns, 48 video tutorials (20 hours) and 39 quizzes spanning the entire curriculum.

 

What are the Mode and Range?

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:

 

The mode of a dataset is the value which appears most frequently.

The range of a dataset is the difference between the maximum and minimum values. 

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!

Key Outcomes

The mode of a dataset is the value which appears most frequently.

If no value appears more frequently than the other values in a dataset, then by definition, the dataset must have no mode.

The range of a dataset is the difference between the maximum and minimum values. 

The range defines an interval within which all other results in the dataset can be found.

Learn About Mode & Range with National5.com

A Powerful New Learning System For National 5 Maths

Our unique learning management system was designed exclusively around the Scottish curriculum. Feature-rich course design gives students the power to tailor their learning, taking advantage of exceptionally detailed explanations, fully worked examples, video tutorials, quizzes and more to identify and tackle problem areas at their own pace.

  • Theory Explanations
  • Intuitive Diagrams
  • Video Tutorials
  • Fully Worked Examples
  • Past Paper Breakdowns
  • Intelligent Quizzes

All hosted in the cloud and accessible anytime on any device.

Learn Anywhere with Unlimited Access

All courses are hosted in the cloud and optimised for use across desktop, tablet and mobile devices. All packages include 1 year’s unlimited access to your chosen course(s).

Our Quality Guarantee

We are so sure you’ll love our course that we offer a 100% money back guarantee. If you’re not entirely satisfied with your course, you can contact us within 14 days of purchase to receive a full refund.

This guarantee is subject to our Terms & Conditions of use.