Mean values and medians are used to represent the mean value and median of a particular area. They are not necessarily directly related to each other, however, since some values tend to be higher than the medians or mean. Mean values are often the only ones used, however. The data can be more complex than just the mean value.
Mean values and medians are important because they help you get a better idea of what average you should use when presenting your data. To do this, you should use an example. For example, the medians for this box plot are divided into three areas. There is a mean, which represents the value used for all the boxes, a standard deviation, which is the arithmetic mean that includes all the values that exceed the mean, and a standard deviation that is an arithmetic mean that excludes any values that fall below the mean. The mean is the average value in the area and the standard deviation is the range of values within the area that exceed the mean.
When graphing your data using these variables, make sure that you graph them all together. Otherwise, you will not have a basis for comparison and analysis between the different variables. For example, you may find that the mean of one area is greater than the mean of another area. However, you cannot use this information to infer that a second area will be greater than the mean of a third area. Similarly, you will not have the statistical power to calculate a range that would allow you to draw comparisons from the different areas. Using multiple sets of data with standard deviations allows you to create a range that allows you to compare the values between the various areas.
The average value is another common variable used in box plots. The average is simply a mean of the mean, so that it is always equal to the mean, but it does not necessarily mean the middle value.
You can use this average to provide support to a hypothesis, but it cannot be relied on as the sole basis. The hypothesis may be true if there is no significant variation between the means of the box plots. However, it is unlikely that it is, as there is a much greater chance that it is false. A second possibility is that the averages are very different from one another, but if they are not, you may need to check more than one set of data.
One way to make sure that the averages in your plot are accurate is to calculate them over a longer period of time. You can calculate the mean of the data over a number of years, or, better yet, use a log scale of the values to see whether they are constant or not. If they are not, then the distributions of data will have become too skewed for a smooth plot, and it may be more difficult to make a meaningful plot out of them.
With these three variables, you will be able to analyze your plot much easier and to provide you with a better foundation for your analysis. You can then proceed with making predictions or conclusions based on your data.
