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


Averages and Range Lessons
4 Part Lesson
Using the Range
4 Part Lesson
Stem & Leaf Diagrams
4 Part Lesson
Median and Mode Averages
4 Part Lesson
Mean Average from Grouped Data
4 Part Lesson
Mean Average from a Frequency Table
4 Part Lesson
Mean Average from Discrete Data
Revision Lessons
Extended Learning
Median and Mode Averages
Extended Learning
Mean from a Frequency Table
Extended Learning
Mean Average
Problem Solving
Grouped Data
Problem Solving
Averages
Revision
Averages and Range
Revision
Estimating the Mean from Grouped 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.
Mean Average
  • 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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