# 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.

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