Desmos for the SAT · Technique 7 of 15
Find Mean, Median, or Standard Deviation from a List
Dump the numbers in, let a formula do the sorting.
When a question gives you a full data set and asks for a summary statistic, mean, median, or standard deviation, Desmos has a built-in function for each.
Type the numbers as a list, wrapped in curly braces, and then call the function you need on that list.
One thing to get right up front: stdev(L1) is the sample standard deviation (it divides by n - 1), while stdevp(L1) is the population standard deviation (it divides by n). If the prompt hands you a full data set or a whole population, reach for stdevp; if it calls the numbers a sample, use stdev.
Nova
Data set questions love to bury one number in a pile of arithmetic, and Desmos just hands it to you. Type the numbers once, call mean, median, or stdev, and the answer pops out while everyone else is still adding.
The algebra way vs the Desmos way
This technique sidesteps adding, sorting, and computing spread by hand.
The algebra way
- Mean: add all five values,
4 + 7 + 7 + 9 + 13 = 40, then divide by 5 to get8. - Median: sort the values to
4, 7, 7, 9, 13and read the middle one,7. - Standard deviation: subtract the mean from each value, square each result, average those squares, then take a square root. Slow and easy to slip on.
The Desmos way
- Type the list once as
L_1 = {4, 7, 7, 9, 13}. - Call
mean(L_1),median(L_1), orstdev(L_1)and read the answer.
The payoff: One function call instead of a page of arithmetic, and for standard deviation that is the difference between a single line and a column of squared differences.
See the move, live
That same example, already loaded in the real calculator, the one built into Bluebook on test day. Try the move yourself.
Before you start: set up Desmos
Convert decimals to fractions
Desmos shows decimals like 1.333. SAT choices are usually fractions. Click the round fraction-converter button next to a value to turn 1.333 into 4/3.
Use subscripts for tables
When building a table for a regression, name the columns x_1 and y_1 so the regression binds to the right data.
Step by step
Nova
Follow along one step at a time, hit Next as you go. I'll flag the spots where people slip.
Type the data as a list using curly braces, e.g. L1 = {4, 7, 7, 9, 13}.
Once you type the list, Desmos labels it an 'N-element list.' Check that N matches how many values the prompt gave before you read any statistic. A skipped comma shows up here as the wrong count, so you catch it early.
Nova: Naming the list L1 up front means you type the numbers exactly once, then reuse it for every stat. Order does not matter, so just enter them as they appear in the question.
![Desmos expression panel showing the list L_1 = [4, 7, 7, 9, 13] typed in.](/_next/image?url=%2Fdesmos%2Fstats-from-list%2Fstep-1.png&w=3840&q=75)
Now try it on a real SAT question
A data set contains the values 2, 6, 7, 10, and 15.
What is the mean of the data set?
Pick an answer to get instant coaching from Nova.
Five numbers is fast to add by hand, but the second the list gets longer or messier, let mean() and median() do the counting for you.
Adding the five values gives 2 + 6 + 7 + 10 + 15 = 40, and 40 divided by 5 values is 8. Typing mean({2, 6, 7, 10, 15}) into Desmos confirms it.
In the app, drills like this adapt to your level, and your AI coach can walk you through any step you get stuck on.
Nova
Five numbers is fast to add by hand, but the second the list gets longer or messier, let mean() and median() do the counting for you.
Set it up yourself in the blank calculator, then read the answer straight off the graph. Muscle memory beats watching.
Watch it
The Desmos trap: when to close the calculator
- If the list is short, four or five numbers, sorting it in your head to find the median is usually faster than typing a list into Desmos.
- Standard deviation questions on the SAT are almost always conceptual, asking which data set is more spread out, not asking for an exact number. You often do not need stdev() at all.
- stdev(L1) gives the sample standard deviation (n - 1). When the prompt describes a whole population, switch to stdevp(L1) (n), or your value comes out a little too big.
Nova
Quick gut-check though: for a tiny list, four or five numbers, finding the median by hand is basically instant. Save the list-typing for when the data set is long or messy enough that hand-sorting would actually cost you time.
Put this move into real practice
"Find Mean, Median, or Standard Deviation from a List" shows up all over the real SAT. SAT Prep Quest drills the skill at your level, so reaching for it becomes automatic by test day.
Practice freeSAT is a registered trademark of the College Board, which was not involved in producing, and does not endorse, this product. Score estimates are Learner Labs projections, not official College Board scores.