Introduction to Exploring Data

Introduction to
Exploring Data

How to Make Statistics Boring

An article published in Teaching Mathematics, June 1996.

Some
Australian Statistics

From Patrick Cook,
Not the News,
The Bulletin,
13 April 1997

Every two minutes, one Australian will feel ill at ease while renting formal wear.

40 million Australians are schizophrenic.

99% of all Australians are abused. Since 90% of abuse is reported to be unreported, this may be just the tip of the iceberg.

And 98% of self-abuse goes unreported.

Statistics and Chocolate

And I'm the .3!

Statistics is a fascinating subject, to both learn and teach! It is also an important one, as we are bombarded with statistics every day of our lives. Knowledge in the subject allows us to make informed judgements about the statistics presented by others to persuade us.

As teachers we need to give our students an understanding of the place of statistics in modern society, an interest in the subject and a solid grounding for further study. It is worth noting that at the tertiary level more students study statistics than study calculus subjects.

Setting the Scene
(from How to Make Statistics Boring)

Ah! I’ll bet some of you thought, ‘Hey, statistics is already boring, it doesn’t need to be made boring." Given the sort of statistics to which we’ve been subjecting ourselves and our students over the years, such an attitude would not be surprising. Consider the following exercise on constructing a boxplot, which is from a popular Math A text.

Construct a box-and-whisker graph for the following data which are the masses in kilograms of nine Year-11 girls:
35 47 48 50 51 53 54 70 75

This was chosen only because it is a typical example of the statistics that many of us are teaching our students. I am not picking on this particular textbook. All of the Maths A and B texts that I have examined are loaded with similar examples. If this exercise doesn’t convince you that statistics can be boring, there are many more where this came from.

Actually, boring is not the most important issue, despite the title. There are other things wrong with this exercise, other than the fact that it is boring. It is trivial. It is pointless. The data are fake.

Source: Boggs, R., (1996). How to Make Statisics Boring, Teaching Mathematics, QAMT, Brisbane.

Themes

One of the first tasks of the statistician when analysing a set of data is viewing the data in a variety of ways, both graphically and numerically, looking for intriguing patterns, unusual observations and the general characteristics of the dataset. This aspect of statistics is a focus of this website.

This website has four underlying themes:

Data should be central to the study of statistics, and our students should study real problems with real data.

Computers and graphing calculators have an essential role in statistics as they excel at drawing graphs and doing calculations. Students should be concentrating on the underlying concepts, looking for patterns and notable features in data, learning to make appropriate decisions on the choice of summary statistics and analyses, and justifying these decisions.

Students need to be actively involved in the study of statistics. Whenever possible, a collaborative, activity-based approach to statistics should be used.

Teachers must know more statistics than that outlined in the syllabus or contained in the textbook. This website has extensive extension material which can give the teacher a broader background to the subject.

Statistics and Chocolate

One of my favourite Internet publications is ZiMaths, which is published by the University of Zimbabwe and which is meant to be 'a device that would educate Zimbabwean schoolkids about the virtues of real maths, as opposed to the spiceless variety taught in most schools'. An article that threads it way through the first three issues follows a bar of chocolate from its raw materials to its marketing, noting how statistics is used in assisting the process. It gives a nice real-world example of queueing, process control, sampling, calibrating machinery, surveying and forcasting.

And I'm the Point 3!

Jane Watson from the University of Tasmania talks on the Australian Broadcasting Corporation's Radio National program about the need for statistical literacy in the Australian community.

From the AP-Statistics Guidebook

I thought this was nicely written, so I will share it with you.

Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. In examining distributions of data, students should be able to detect important characteristics, such as shape, location, variability, and unusual values. From careful observations of patterns in data, students can generate conjectures about relationships among variables. The notion of how one variable may be associated with another permeates almost all of statistics, from simple comparisons of proportions through linear regression. The difference between association and causation must accompany this conceptual development throughout.