Error bars are graphical representations of the variability of data.
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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.
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.
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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.