How to find mean, median & standard deviation on Desmos
Digital SAT statistics questions live or die on one move: getting your numbers into a list. Once the data is typed in, Desmos hands you the center and spread before you'd finish doing it by hand.
Type your data set on one line as a list — for example L=[4,7,7,9,13] — then on the next lines call the built-in functions: mean(L), median(L), and stdev(L) (sample) or stdevp(L) (population). Add min(L), max(L), total(L) and count(L) for range, sum and count. For a frequency table, repeat each value as many times as its frequency. Every result updates the instant you edit the list.
stdev divides by n−1; stdevp divides by n.From a row of numbers to every statistic
Eight keystroke-level steps. Once you've done this a few times, the whole thing takes seconds — type the list, read the stat the question asks for.
Start a fresh line
Click an empty row in the expression list on the left. Each statistic gets its own line, so results stack neatly under your data.
Name and type the list
Give the data a short name and type the values in square brackets, separated by commas: L=[4,7,7,9,13]. Repeated values are fine and expected.
Get the mean
On the next line type mean(L). Desmos prints the average immediately — this is the "average," "arithmetic mean" or "expected value" the question may ask for.
Get the median
Type median(L) for the middle value of the sorted data. You don't have to sort by hand — Desmos orders the list internally.
Pick the right spread
Type stdev(L) for the sample standard deviation or stdevp(L) for the population one. The wording tells you which group the numbers represent.
Grab range, sum and count
Use min(L) and max(L) for the range (their difference), total(L) for the sum, and count(L) for how many values are in the set.
Expand a frequency table
If a table says a value of 6 appears 3 times, type 6,6,6 inside the list. List every value its number of times, then run any function as usual.
Stress-test it
Change one number — say swap 13 for 99 — and watch which results jump. This is the fastest way to answer "how does adding this value change the mean/median?"
Mean vs median when an outlier arrives
A classic SAT setup: a small data set, then one value gets much bigger. The trick is knowing which measure moves and which barely budges.
The number of books five students read over the summer is 4, 7, 7, 9, and 13. A sixth student is added who read 50 books. How does adding the sixth student affect the mean and median of the data?
Set up the original list. Type A=[4,7,7,9,13]. Then mean(A) returns 8 (the total is 40, divided by 5), and median(A) returns 7 — the middle of the five sorted values.
Add the outlier and recompute. Type B=[4,7,7,9,13,50]. Now mean(B) returns 15 (total 90 over 6 values). For the median of an even-sized set Desmos averages the two middle numbers, 7 and 9, so median(B) returns 8.
Compare the shifts. The mean leapt from 8 to 15 — a jump of 7. The median moved only from 7 to 8 — a jump of 1. The single large value dragged the mean far more than the median, so the correct answer is the mean increases much more than the median.
Why the median holds steady
The mean depends on every value, so one large number inflates the sum and pulls the average toward it. The median depends only on the position of the middle value, so a far-off number changes it slightly at most. That's why test-writers call the median "resistant" to outliers — and why a question that adds an extreme value is almost always testing this distinction.
Speed tip: keep both lists on screen at once (A and B) so the before-and-after results sit side by side and you can read the change at a glance — no re-typing.
Make it a reflex, dodge the traps
Any time you see a data set.
Five numbers or fifty, a raw list or a frequency table — typing it once and calling mean(), median() and stdev() is faster and safer than adding and sorting by hand.
Sample vs population, and frequencies.
Choosing stdev when the question wants stdevp changes the answer. And forgetting to repeat values from a frequency table silently undercounts your data — double-check count(L) matches the table total.
When no calculation is needed.
Some "which measure is larger?" or "what happens to the spread?" questions can be reasoned out from the shape of the data. If you can see the answer, don't bother typing — but Desmos is there to confirm in two seconds if you're unsure.
Drill these on SAT-style stats.
The setups only stick when you use them on real questions with the built-in calculator, until typing the list is automatic.
Desmos statistics on the SAT, answered
How do I enter a data set in Desmos on the SAT?
L=[4,7,7,9,13]. That single list then feeds every statistics function — mean(L), median(L), stdev(L) and so on.What is the Desmos command for mean and median?
L, type mean(L) for the average and median(L) for the middle value. Desmos updates the result instantly as you edit the list.Should I use stdev or stdevp for standard deviation?
stdev(L) gives the sample standard deviation (dividing by n − 1) and stdevp(L) gives the population standard deviation (dividing by n). Read the question: SAT items usually treat the listed numbers as the whole group, but check the wording, and confirm current function behavior on the official sites.How do I handle a frequency table in Desmos?
6,6,6 — then run mean() or median() on that list. For larger tables you can build a weighted list, but repeating the values is the simplest reliable method. Verify count(L) equals your table's total.Why does an outlier change the mean more than the median?
More Desmos moves for SAT Math.
Turn data sets into easy points.
Start free and practice SAT-style statistics with the built-in calculator, until entering a list and reading the answer is automatic.