Desmos for the SAT · Technique 20 of 23
Find Mean, Median, or Standard Deviation from a List
Type the numbers once as a list, then let a function do the sorting and the arithmetic.
Watch the lesson
The whole move worked on one real SAT question, narrated.
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 square brackets, and then call the function you need on that list. Square brackets, not curly braces: a curly brace means a restriction in Desmos, so L1 = {4, 7} builds no list at all and every statistic you ask for comes back blank.
Desmos has two standard deviation functions, stdev(L1) and stdevp(L1), which divide by slightly different counts. The SAT does not ask for a standard deviation as a number, so the difference rarely matters. When a question compares the spread of two data sets, either function gives the same comparison, as long as you use the same one on both lists.
Nova
Data set questions hide one number behind a lot of arithmetic, and Desmos hands it to you. Type the numbers once, call mean, median, or stdev, and the answer is there before you would have finished adding.
Now you try it
The rest of the page takes that move slowly. First how it compares with doing the algebra, then the steps in order, then a real SAT question with a live Desmos calculator to try it in.
The algebra way vs the Desmos way
This technique sidesteps adding, sorting, and computing spread by hand.
The question
Data set: 4, 7, 7, 9, 13, 13, 14, 16, 18, 21, 22, 27
What is the median? The same list also hands over the mean and the standard deviation.
The algebra way
- Mean: add twelve values without slipping, then divide by 12.
- Median: sort all twelve, then average the sixth and seventh because there is no single middle value.
- Standard deviation: twelve differences, twelve squares, an average and a square root. Minutes, not seconds.
The Desmos way
- Type the list once as
L_1 = [4, 7, 7, 9, 13, 13, 14, 16, 18, 21, 22, 27]. - 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. At twelve values the by-hand path is minutes and the typed one is seconds.
Step by step
The whole move, all 4 steps
- Type the data as a list in square brackets,
L_1 = [...]. Brackets, never braces. - On the next line type
mean(L_1)for the mean. - Use
median(L_1)for the median, andstdev(L_1)for the standard deviation. - Read the result Desmos prints next to the expression.
The question
A data set contains the twelve values 4, 7, 7, 9, 13, 13, 14, 16, 18, 21, 22, 27.
What is the median of the data set?
- A13
- B13.5
- C14
- D14.25
Step 1 of 4
Type the data as a list in square brackets, e.g. L1 = [4, 7, 7, 9, 13, 13, 14, 16, 18, 21, 22, 27].
Naming the list L1 up front means you type the numbers exactly once, then reuse it for mean, median and stdev. Order does not matter, so enter them as they appear in the question.
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. On a twelve-value list a skipped comma is easy to miss, and this count is what catches it.
Now try it on a real SAT question
Head or scratch paper. Seven values, already in order. Count in to the fourth one and you are done before the calculator loads. Type it in afterwards if you want the check.
A data set is shown: 2, 2, 2, 3, 4, 4, 11.
What is the median of the seven data values?
Pick an answer to get instant coaching from Nova.
Seven values in order. Which position is the middle one, and is the list already sorted?
Seven values in order, so the median is the fourth: 3.
In the app, drills like this adapt to your level, and your AI coach can walk you through any step you get stuck on.
Set this question up yourself, then read the answer straight off the graph.
Worked it out on scratch paper? Type it into Desmos anyway and check. It takes a couple of seconds and it catches the slip you cannot spot by re-reading your own work.
The Desmos trap: when to close the calculator
- If the list really is short, four or five numbers, sorting it in your head to find the median is faster than typing it in. The typing pays off once the list is long enough to lose track of.
- 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.
Nova
For a tiny list, four or five numbers, finding the median by hand is 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.