Standard Deviation:

Desmos has many powerful functions and features, and it has extensive statistical capabilities, including a built-in function STDEV() (or STDDEV()) for computing the sample standard deviation and STDEVP() (or STDDEVP()) for computing the population standard deviation of a data set.

Most often, however, the digital SAT will only ask you to compare the standard deviation of two data sets, and it will always present the data in such a way that this determination can be instantly made merely by inspecting the provided table(s) or chart(s); on rare occasion, however, you might be asked to find the actual standard deviation of a data set, so you should know that the STDEV() and STDEVP() functions exist.

Of course, it would be possible to make the needed comparison between the standard deviation values for two data sets by actually calculating the standard deviation values for each data set and then comparing those values. However, the data is invariably provided as frequency tables (or, equivalently, as histograms or dot plots), and you cannot apply the STDEV() function to a frequency table; Desmos also has no built-in mechanism for converting a frequency table to a data set, so the only option would be to manually enter the data set corresponding to a provided frequency table or chart, and that would always be exceedingly time-consuming due to the number of values involved.

Here's an example that illustrates this point:

This problem asks about both the range and the standard deviation of the data sets; the range is easily determined mathematically by subtracting the smallest represented data value from the largest in each set, and we want to focus on what the task would look like if we wanted Desmos to calculate the standard deviation of each data set. As noted, this would require decomposing each dot plot into the data set it represents so that we can apply the STDEV() function. Take a look at how tedious this procedure would be to undertake.

Answer: A

Even with optimal cutting and pasting, this still takes quite a lot of time to set up, and the chances for error increase with each additional item that must be included in a solution setup. Our advice: learn to recognize relative standard deviations from data presented in frequency tables, dot plots, and histograms, and don't turn to Desmos for help unless you are completely clueless—and have lots of extra time.

Coda:

For those who might be wondering whether a frequency table can be converted into a data set using Desmos, then answer is yes, but there's no quick way to implement this conversion. Below we present a solution for the above example; we use a function we created for performing the conversion, and as you can see, it's relatively elaborate and certainly not something you would bother to memorize and reconstruct while taking a real test. We enter the dot plots as frequency tables, supply our conversion function, then apply the STDDEV() function to the resulting data sets.

Here's the function we wrote to convert a frequency table to a data set; it's the third entry in the Desmos graph below:

The lesson is clear: just because you can, doesn't mean you should (aka f() around and find out).