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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Discussing Sample Displays

Inference HOME | Achievement Objectives | Overview | Statistical Cycle
- Write an introduction | Using NZgrapher | Discussing sample statistics
- Box plots | Discussing the boxplot & dotplot | Sampling methods | Sample variability and size
- Informal confidence interval | Comparing two populations - discussion
- Writing a report | Revision


Discussion of Sample Displays

When describing dot plots: discuss symmetry, skew, outliers, gaps, clusters
Also consider possible reasons or causes of these features (in the context)

Box and whisker: Summary statistics, symmetry, skew

It there are sub groups or a second variable using different colours to show this, and discuss as well.

“In my sample...”
“The sample boxplot suggests...”
“I notice that...”
“From the boxplot I notice...”

The discussion needs be in context at all levels. The context includes the variable, for example height, numerical values and associated units and the population groups.
eg The heights of NZ year 12 boys and NZ year girls.

Class notes, Blank notes

Activity: Box plot discussing Quiz on
centrality | Spread | Symmetry | Tail length | Histograms & Box plots (considering outliers) (links to Murdoch University)

Distribution Sample Shapes.pdf (link to Census at schools)

Worksheet and answers on 'What I notice about a distribution' (link to mathstatsfacilitators web site)


Dot plots

Symmetry - Is the data symmetrical either side of the median? Or is one side more spread out?

Skew - Data spreading right is right skewed 

Outliers - Any data more than 1.5 ‘boxes’ above UQ is an outlier. Data more than 3 ‘boxes’ above UQ is extreme (see later notes)

Gaps - A small gap is of no concern, but a large gap may reflect groups or underlying variables

Clusters - A bunching of data in one region


Box Plots

When describing Box and whisker: Summary statistics, centrality, spread, symmetry, skew, tail length

Summary statistics (Review) – do not discuss Max or Min (irrelevant)

Discuss the ‘middle 50%’ ie the ‘box’ and median If comparing samples discuss overlap and shift (eg distance between medians)

Show groups or a second variable using a different group colour. Discuss these groupings  

Initial interpretation
Centre (middle 50%)
Unusual aspects
Shift / Overlap

And for merit things like: ‘I notice ...  I expected ...  I was surprised that...’
Also consider possible reasons or causes of these features (in the context) (Merit & Excellence)



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