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Module 2 · Statistics Foundation

Descriptive statistics.

This module teaches students how to describe data clearly before moving into probability and inference. You will learn how to summarise centre, spread, position and shape, then bring those ideas together to compare groups responsibly.

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5

Lessons

8–9 hrs

Study time

0

Coding

Foundation

Level

What this module builds

The practical language of data summaries.

This module moves from individual summaries to complete distribution thinking. Students learn that a good description of data should mention what is typical, how much values vary, how values are positioned, what the shape looks like and how groups compare.

Centre

Understand how mean, median and mode describe typical values, and why the most appropriate centre depends on variable type, skewness and outliers.

Spread

Learn how range, IQR, variance and standard deviation describe consistency, dispersion and variability around the centre.

Position

Use ordered data, quartiles, percentiles and five-number summaries to describe where values sit inside a distribution.

Shape

Recognise symmetry, skewness, clusters, tails and unusual observations before choosing final summaries.

Comparison

Compare groups descriptively using centre, spread, shape, overlap and cautious interpretation.

By the end

Students should be able to describe data responsibly.

1

Choose mean, median or mode based on data type and shape.

2

Interpret range, IQR, variance and standard deviation.

3

Use quartiles, percentiles and five-number summaries.

4

Read boxplots as summaries of centre, spread and outliers.

5

Recognise symmetric, skewed, clustered and outlier-affected data.

6

Compare groups using centre, spread, shape and overlap.

7

Write careful descriptive conclusions without unsupported causal claims.

Descriptive workflow

Ask four questions of every dataset.

The module trains students to avoid one-number summaries. A good descriptive analysis asks about centre, spread, position and shape before making comparisons.

What is typical?

Use the mean, median or mode to describe the centre, but choose the measure carefully.

How variable is it?

Use spread to decide whether the data are consistent, dispersed or unstable.

Where are the middle values?

Use quartiles and percentiles to describe ordered position and the middle 50%.

What is the shape?

Check skewness, tails, clusters and outliers before trusting a single summary.

Module lessons

Study the lessons in order.

Each lesson is built as a full learning experience with lecture, detailed notes, interactive lab, worked examples, practice, reflection and quiz. The lessons build from single summaries to full group comparison.

2.1

90–100 min
ExpandedTypical values

Measures of centre

Learn how the mean, median and mode represent different ideas of a typical value, and how outliers and skewness affect the best choice of centre.

Mean vs medianModeRobust centre

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2.2

100–105 min
ExpandedVariability

Measures of spread

Understand range, interquartile range, variance and standard deviation as ways of describing consistency, dispersion and uncertainty in data.

Range and IQRVarianceStandard deviation

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2.3

100–105 min
ExpandedPosition

Quartiles, percentiles and five-number summaries

Study how ordered data can be divided into positions, quartiles, percentiles, five-number summaries, boxplots and outlier fences.

QuartilesPercentilesBoxplots

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2.4

100–105 min
ExpandedDistribution shape

Shape, skewness and outliers

Learn how distributions can be symmetric, skewed, heavy-tailed, clustered or affected by unusual observations, and how this changes interpretation.

SkewnessOutliersShape diagnosis

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2.5

105–110 min
ExpandedGroup comparison

Comparing groups descriptively

Bring centre, spread, shape, quartiles and graphical summaries together to compare groups carefully without overclaiming.

Group summariesOverlapCareful reporting

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How to study this module

Do the visual labs slowly.

The interactive labs are designed to build statistical judgement. Move the controls, compare the summaries, read the interpretation panel and write one sentence about what changed. This is how centre, spread, position and shape become meaningful.

Module completion

Ready for probability foundations.

After these five lessons, students should be able to describe a dataset clearly and compare groups responsibly. The next module can then introduce probability as the language of uncertainty.

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