Vary Useful Statistics

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Vary Useful Statistics

Introduction

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Activities

STEPS
Tutorials

Interactive computer-based tutorials

Worksheets

Measures of Spread

Statistics are like a bikini; what is revealed is interesting, what is concealed is crucial.

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

FYI

I'm Not Mad about MAD

A statistician with hair on fire and feet in a block of ice on average is doing just fine!

Ticky-Tacky Boxes

78.46% of all statistics are made up on the spot.

The measure of spread of a dataset is a vary useful statistic!

When summarising a dataset, at least two measures are needed - one to locate the dataset and another to indicate the spread of the data. The mean and the median are the common measures of location, while the standard deviation and interquartile range are commonly used to summarise the spread of the data.

Range

One measure of the usefulness of a statistics is its robustness. A robust measure is one that is little affected by outliers. On this basis the range, which is simply calculated as

Range = largest data value - smallest data value

is obviously not very robust and hence is not particularly useful.

Mean Deviation

Until recently I was never able to satisfactorily answer the question, "The mean deviation is simple. Why is the standard deviation used rather than the mean deviation?" An email by Paul Gardner from Monash University gives a clear explanation, and is the basis of the article, I'm Not Mad about MAD.

Standard Deviation

The Measures of Spread worksheet contains some lovely questions on standard deviation, courtesy of Pat Ballew. In fact I would rate these questions as being at least 1.5 standard deviations above the average question.

Interquartile Range

The interquartile range, while simple in concept, has caused much grief to introductory statistics teachers since different respectable sources define it in different respectable ways! The article Ticky-Tacky Boxes discusses the different methods of finding Q1 and Q3, in the context of constructing a boxplot, and makes a recommendation as to which is 'best'.

STEPS

The STEPS modules are a collection of hypertext-based tutorials covering a wide range of statistics topics, including summary statistics. Visit the STEPS page for further information and a list of the modules available.

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