What shows how the data set is spread around the mean?

Answer 1

>>variance While it is true that, in many cases, variance does provide a good deal of information, particularly for statistical analysis, in many situations e.g. when the data is not normal, there are only a few points in a data set, or one wishes to examine only a single data set many other properties can be considered.

Specifically, it is often very useful to look at the median as well as the interquartile range. Quickly, just in case, the median is, after the data is sorted, the middle number. The inner quartile range is the difference between the value at the 75th percentile and the 25% i.e the range of the middle 50%. What is nice about these two values is that they eliminate outliers (numbers which are, for whatever reason, exceptionally large or small compared to the data set) and gives a better idea of where the data lies. The mean cannot account for large outliers and, for small data sets, can differ significantly from the median. While statistical analysis is more limited with the median, it can often be a more accurate representation of a population.

As an example, income reports very dramatically when looking at the difference between variance and inner quartile range. Because the median US income is far below the mean income (i.e. there are a small group of VERY wealthy people, thus the mean is pushed above the median) the inner quartile range is more informative that the variance. This is especially true on the micro level when e.g looking by county.