# Working with data

## 1.1.1 State that error bars are a graphical representation of the variability of data.

Error bars are graphical representations of the variability of data.

## 1.1.2 Calculate the mean and standard deviation of a set of values.

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## 1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean.

The term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean. This rises to about 95% for +/- 2 standard deviations.

## 1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.

The standard deviation is used to show how the values are spread above and below the mean. A low standard deviation means that the values are closely grouped around the mean whereas a high standard deviation means that the values are widely spread. About 68% of the values fall within one standard deviation of the mean. This rises to about 95% for +/- 2 standard deviations.

We can use the standard deviation to decide weather the differences between two means is significant. If the difference between the two means is larger than that of the standard deviations then the difference between the two means is significant. If the difference between the two means is smaller than that of the standard deviation then the differences between the two means are insignificant.

## 1.1.5 Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.

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## 1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables.

Correlation often shows a casual relationship between two variables such as height and weight. Taller people tend to be heavier and so we can see a correlation in these two sets of data. However, some variables may show correlation when in fact there is no casual relationship between them. The results may be correlated by chance. This means that even the correlation is a useful tool for studying data, it is not always reliable.