Statistics Shortcuts
Desmos has built-in statistics functions. On SAT data-interpretation questions, let it do the arithmetic.
Core statistics functions
Type any of these directly in an expression line. Data can be a list in brackets or a table column.
mean([1,2,3,4,5]) returns the arithmetic mean.median([1,2,3,4,5]) returns the median.stdev([...]) or stdevp([...]), sample vs. population standard deviation. (SAT usually uses stdev.)quartile([...], 1) returns Q1. Use 2 for median, 3 for Q3.total([...]) sums a list.count([...]) counts items.min([...]), max([...]), extremes.
Using a table column directly
When you have a table with column $x_1$, you can pass it to any stat function: mean(x_1), median(x_1), stdev(x_1).
This lets you copy data into a table once and reuse it across several calculations.
Worked example: mean and median from a table
Problem: A store sells daily. The last 7 daily totals (in dollars) are:
$120, 145, 160, 112, 190, 175, 155$.
What is the mean? What is the median?
- Create a table. Enter the 7 values in $x_1$.
- New expression:
mean(x_1). Output: $151$.
- New expression:
median(x_1). Output: $155$.
Answers: mean $= 151$, median $= 155$.
Worked example: "which change affects the mean more"
Problem: A teacher's class has test scores $\{65, 72, 78, 81, 85, 88, 92, 95\}$. If one score of $65$ is replaced with $95$, by how much does the mean change?
- Create a table, enter the original 8 scores in $x_1$.
- Expression:
mean(x_1). Output: $82$.
- Edit the $65$ cell to $95$. Mean recomputes live. New output: $85.75$.
- Change = $85.75 - 82 = 3.75$.
Answer: increases by $3.75$.
Worked example: standard deviation comparison
Problem: Two data sets:
A: $\{10, 10, 10, 10, 10\}$
B: $\{6, 8, 10, 12, 14\}$
Same mean. Which has the larger standard deviation?
- Expression 1:
stdev([10,10,10,10,10]). Output: $0$.
- Expression 2:
stdev([6,8,10,12,14]). Output: $\approx 3.16$.
Answer: set B. (Intuition: same mean, more spread.)
On the SAT, you usually don't have to compute $\sigma$ from scratch, the question often asks for comparison. Desmos confirms in 5 seconds.
Worked example: margin of error / confidence interval
If a question gives you a mean and standard deviation and asks for the range within one standard deviation, just compute:
mean(x_1) - stdev(x_1) → lower boundmean(x_1) + stdev(x_1) → upper bound
Same with two SD for 95% approx range. No need to memorize formulas.
Common traps
Watch for these gotchas
- Sample vs. population SD. SAT problems usually treat the given list as the whole population, use
stdevp if they specify. stdev is the more common SAT answer.
- List syntax. Use brackets and commas:
[1,2,3]. Parentheses don't work.
- Don't lose the table mid-question. If Desmos closes the calculator between questions, your data is gone. Screenshot or retype, but honestly, the Bluebook app preserves it across the module.
Try it yourself
Practice problem
A student's seven quiz scores: $82, 85, 90, 75, 88, 92, 80$. Compute the mean, median, and standard deviation using Desmos, no pencil.
Show answer
Steps: New line: mean([82,85,90,75,88,92,80]). Output: $\approx 84.57$.
median([82,85,90,75,88,92,80]). Output: $85$.
stdev([82,85,90,75,88,92,80]). Output: $\approx 6.05$.
Answer: mean $\approx 84.6$, median $= 85$, SD $\approx 6.1$.
You've finished the Desmos walkthroughs
Next: put it to work. Every Math practice session in the workspace lets you keep Desmos open in another tab (or on a phone if you're practicing offline). The more you use it on practice, the faster it'll feel on test day.
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