# Averages and Range

Students learn how to calculate the mean, median, mode and range of discrete and continuous data.  They use these to compare distributions and analyse sets of data.  Learning progresses from working with data in a list to data presented in a grouped frequency table.

This unit takes place in Year 9 Term 3 and is followed by representing data

##### Prerequisite Knowledge
• Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

##### Success Criteria

interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:

• appropriate graphical representation involving discrete, continuous and grouped data
• appropriate measures of central tendency (median, mean, mode and modal class) and spread

apply statistics to describe a population

##### Key Concepts
• It helps to teach students to associate the sound of median and mode to middle and most.
• The range is not an average but a measure of spread.
• Illustrate the concept of the mean average as shown below.

• A frequency table is used when the sample size increases beyond simple calculations being possible from a list.
• The median average of a class width is used as the mid-pint when calculating the mean from grouped data.

##### Common Misconceptions
• Students tend to confuse the median, mode and mean averages.
• The range is often incorrectly thought of as a type of average.
• Students often find it difficult to calculate the median average from data presented in a frequency table.
• When sorting continuous data into a grouped data table students often struggle to fully understand the inequality notation.

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Mr Mathematics Blog

#### Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

#### Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

#### Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]