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# Misunderstandings

Throughout each stage of a statistical investigation there are likely to be times where either inadequate understanding or a misunderstanding hinders progress.

At the beginning of an investigation, inappropriate sampling can put an entire investigation into jeopardy. Students can believe that any sample is adequate as long as the data are collected carefully. They can be unaware of the importance of sample size, the possible impact of biased sampling and the extent of the representative nature of the sample.

Graphs are a powerful way to represent data but inappropriate graphs can be misleading. It is important for students to be exposed to a number of different types of graphs, including those that are deceptive.

It is important to summarise data in a way that accurately characterises the data set. Students can choose inappropriate statistical measures and/or misunderstand the extent to which they apply.

Informal inference uses evidence from a sample to draw conclusions about a wider population. Students can misunderstand the relationship between samples and populations. They can also lack experience in judging the significance of differences between two data sets or the strength of an association.

Finally, through lack of experience with statistics and unquestioning belief in the media, students may be being misled on social issues.

## Misunderstanding samples and sampling

Inappropriate sampling methods and sample sizes can detract from the credibility of the conclusions drawn from a statistical investigation.

## Misleading graphs

Graphs can sometimes tell a misleading story. To get the truth about the data, students need to become graphical sleuths.

## Misunderstandings of averages

An average is a measure of a typical value of a data set. The curriculum focusses on mean, median and mode as measures of centre or averages.

## Difficulties with informal inference

Informal inference is about making decisions, often in comparing two data sets or judging the strength of an association. Without formal criteria this process can be difficult.

## Belief in the media

Headlines in the media are meant to attract attention but can we believe them? How much do they exaggerate?