Mean, Mode and Median
Students often learn how to calculate measures of central tendency but do not really understand what they are doing or what information they are looking for. Use context from the area you are working with to discuss the purpose of a statistical measure. With students, establish and use criteria which can be applied to evaluate the validity of the measure being used. This link gives a concise summary of the different averages, when to us them and when not to!.
http://www2.le.ac.uk/offices/ld/resources/numerical-data/averages
You could provide examples from science of the same data processed using different measures of average and spread and ask students to apply clear criteria to decide on the most appropriate measure given the context.
The need to be familiar with these different calculations is most likely to likely to occur in the Quantitative Chemistry section, Ecosystems and Biodiversity in Biology as well as in the Forces and Motion section of physics (stopping distances, everyday road transport).
Using class variation data to explore mean, mode and median
Using numbers from the CensusatSchool data sets, this teaching pack has some nice data about the physical characteristics of students in schools that could be used to support calculations that you carried out yourself as well as an interesting way to look at variation in humans. Looking at data sets of like this is perhaps the most common and accessible way that these mathematical calculations will be used in Biology. (The data set in on page 9, good questions on page 12).
How to Find the Mean
This link gives a concise summary of how to calculate the arithmetic mean. It also includes an explanation of why it works as well as some ideas to challenge learners and a visual demonstration to support learners which are struggling. There are also a set of questions to choose from to check students prior understanding.
Understanding Mean, Median, Mode and Range S4
In this DfE Standards Unit resource, students learn to understand the terms: mean, median, mode, range and explore the relationships between these measures and their relationship to the shape of a distribution. Students will have met the terms mean, median, mode and range but they may not have a clear understanding of their meaning and the relationships between them. One purpose of this session is to expose and discuss any misconceptions.
The resource starts with a quick activity to check pupils’ prior understanding of mean, mode, mean and range. this is described on page 2.
Students then work in pairs to match pairs of cards one set has charts the other statistical measures. They will notice that some of the Statistics cards have gaps on them and one of the charts is blank. Learners should try to work out what these blanks should be. The resource suggest some probing questions you can use to help challenge/support learners
Statistical Calculations
These nine instant maths ideas explore a variety of statistical calculations. The first task asks students to discuss a spider diagram depicting descriptive statistics. Other tasks explore misconceptions when calculating different averages and consider which average is the most appropriate to use in different situations.
Student resource sheets to accompany the tasks include:
• a task sheet containing probing questions on mean, mode and median
• a task sheet in which students state whether the given statements are possible or impossible when considering mean, mode, median and range
• a sheet describing the advantages and disadvantages of the three different ways of calculating an average
• a source sheet containing different journey times
• a sheet explaining how to find a variety of different statistical calculations.
