What does a high standard deviation indicate?

A high standard deviation indicates that the data points are spread out widely from the mean.

In more detail, standard deviation is a measure of how much the values in a data set vary from the average (mean) value. When the standard deviation is high, it means that the data points are not clustered closely around the mean but are instead spread out over a wider range of values. This suggests greater variability or diversity in the data set.

For example, imagine you have two sets of test scores. In the first set, most students scored between 70 and 90, while in the second set, scores ranged from 40 to 100. The second set would have a higher standard deviation because the scores are more spread out.

Understanding standard deviation helps in analysing the consistency of data. In a classroom setting, if test scores have a high standard deviation, it might indicate that some students are performing very well while others are struggling. Conversely, a low standard deviation would suggest that most students are performing at a similar level.

In summary, a high standard deviation reveals that there is a lot of variation in the data, which can be useful for identifying patterns, making predictions, and understanding the reliability of the data.