### WolframAlpha as an on line statistics calculator

With the up front proviso that due to sample size limits WolframAlpha is only useful in a classroom situation, WolframAlpha provides a quick first statistical look at data. Given the input {29, 30, 53, 75, 89, 34, 21, 12, 58, 84, 92, 117, 115, 119, 109, 115, 134, 253, 289, 287}, WolframAlpha returns basic statistical facts about the data. Note the absence of any command word in that input.
Ideally one would probably like to see a box-and-whickers plot along with a normal probability plot to determine from the get go whether one can use normal curve or t-distribution statistics on the data. That was my original quest - a one stop single entry site where one could enter data as a comma delimited list and the site would automatically spit out all the basic descriptive statistics one might want to see.

And while there are some excellent on line calculators worth exploring such as Alcula and Cooldivs, the former having a nice box plot option, almost all of the on line calculators are "single purpose." When fed data they spit out only a single outcome - such as a box plot. Or mode, median, and mean. Or a histogram. But not a smorgasbord of commonly looked at analyses. One has to run multiple calculators to get the quick overview.

Of course there are powerful downloadable statistical environments such as R which include strong GUIs on Ubuntu, but students cannot usually install software on the computers on which they are working. My logic has always been to teach students tools that they can find and use "in the wild" - even after they graduate. Alumni are not likely to have administrative privileges on work computers that they use, so I opt for tools that they either have or can use without admin privileges.

WolframAlpha has potential as a first look at small data sets. Even the default output, seen in the images above, provides a number line and histogram that give first indications of the nature of the data. There is, however, more available upon request. Click on the "More" button and WolframAlpha will list the first and third quartile, the interquartile range, skewness, kurtosis, and normal curve confidence intervals.
Note that one can also generate the t-intervals. There is still a "More" button, a second press of that button lists more than the basics. At this point one should have a fair idea whether the data is reasonably normal. If so, one can use the t-intervals to run a hypothesis test using the confidence interval for alpha equals 0.10 or 0.05. The second iteration of the "More" button also adds an alpha of 0.01.

If the data is heavy tail or highly skewed, then one will have to move on to more sophisticated software packages. For the above data bootstrap methods are an appropriate way to find the asymmetric 95% confidence interval. But as a first look WolframAlpha provides a nice set of charts and basic data exploration statistics.

Post-script: The result of the second press of the "More" button.