A commonly encountered task given a data set is to summarize the data by calculating their 'mean'. Generically speaking, a mean is a value which is as close or closer to the data 'on average' than than any other value for a given measure of distance. For the ordinary Euclidean distance (mean-square, p=2), this value is the garden variety arithmetic mean. For the mean absolute deviation (p=1), it is the median of the data. For the maximum absolute deviation (p=infinity,the uniform norm), it is the midrange. For other p's, the answer does not have a convenient, closed-form description. The app computes the 'mean' for all values of p in the range 1 to 100, as well as p=infinity. Click on the following link for a more mathematically complete description.
Enter the data in one of two ways: (1) By hand (typing them in in the field provided) or (2) Upload the data as a column in a csv file.
Now use the bar below to select p for Lp-distance/mean. Default is p=2. Graphs of t vs. Lp-distance are under 'View' tab. Repeat. Each value of p is saved along with minimizing value for the data and that p. A downloadable table of these values can viewed under the final tab.
Use the plot below shows the data (horizontal axis) and a plot of t vs. mean Lp-distance to t. Minimizing value of t is shown in red.
In the dialogue box, enter up to four values for p. Hit 'Enter'. The plot shows the minimization curves for the data and those p's and the mean, median, and midrange for the data.
Summary statistics for the current data set.
A downloadable table of selected p's and corresponding minimizing values for the data.