Comparing and Summarising Data

Finding the median and mode averages

How to calculate the mean average

Mean average and range

Stem and leaf diagrams

Comparing stem and leaf diagrams

Prerequisite Knowledge

• Solve comparison, sum and difference problems using information presented in a line graph
• Complete, read and interpret information in tables, including timetables.
• Interpret and construct pie charts and line graphs and use these to solve problems
• Calculate and interpret the mean as an average.

Key Concepts

• The mode is the most common item in a set of data.  It is the only average that can be used for qualitative data.  A data set can have two modes.  This is called bi-modal.
• People often refer to the mean when using the word ‘average’.  It is the sum of the data divided by the sample size.  The mean takes into account every piece of data.
• The median is the middle number when all the numbers have been put into ascending order.  The median can be between two numbers.
• The range is the difference between the largest and smallest data values.  The range is a measure of distribution or consistency.
• To compare data sets students should use the range and one or more of the averages.
• A key is critical to interpreting stem and leaf diagrams.

Working mathematically

Develop fluency

• Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

• Explore what can and cannot be inferred in statistical settings, and begin to express their arguments formally.

Solve problems

• Begin to model situations mathematically and express the results using a range of formal mathematical representations.

Subject Content

Statisitics

• Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)