# Representing and Interpreting Statistical Diagrams

Students learn how to choose and then plot the most appropriate representation for a set of data.  As learning progresses they interpret a range of statistical diagrams to compare multiple distributions.

This unit takes place in Term 2 of Year 8 and follows on from Comparing and Summarising Data.

##### Prerequisite Knowledge
• 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)
• Interpret and construct pie charts and line graphs and use these to solve problems
• Calculate and interpret the mean as an average.
##### Key Concepts
• A pie chart displays data when you want to show how something is shared or distributed.
• The angles at the centre of a pie chart have a sum of 360°.  The angles are used to represent the frequency or proportion.
• To compare data sets using pie charts use the angles to compare the proportions and frequencies to compare the area.
• Continuous data can be arranged into a frequency table.  The class intervals using inequality notation to ensure they do not overlap.
• A frequency polygon joins the midpoints of the top of the bars with a straight line.
• Scatter graphs show the correlation between two variables.  If there is a reasonable correlation a line of best fit can be drawn.  There should be approximately the same number of points on each side of the line of best fit.
##### Working mathematically

Develop fluency

• Use language and properties precisely to analyse statistics.

Reason mathematically

• Explore what can and cannot be inferred in statistical and probabilistic 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
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
##### Subject Content

Statistics

• Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
• Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

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