🧮 Desmos for statistics

Every calculation in MAT 300 is a list plus one function. Here are all of them, with copy-ready recipes.

You do not have to leave the site. The 🧮 Statistics calculator page does the same jobs in the page — paste a list and it gives you the summary, the histogram, the box plot, outliers, the line of best fit, confidence intervals and tests. Desmos is still worth knowing for the exam, so both are here.

⭐ The one idea

Desmos does every calculation in MAT 300. You type a list (or a table), then call a function on it. Learn the 12 functions below and every exam question becomes typing, not arithmetic. Open it at desmos.com/calculator.

⌨️ Typing tips that save you on the final

📋 Lists

Square brackets, commas: L = [92, 98, 104]. Name it a capital letter so you can reuse it. [1,...,20] makes 1 to 20.

📊 Tables

+ → Table. Columns are automatically x₁ and y₁ — those names work in any function. Paste a column straight from a spreadsheet.

✖️ Symbols

Square root: type sqrt. Power: ^. Infinity: infty. Plus-minus: pm. Subscript: _ (x_1). Regression tilde: ~.

🔢 Decimals

Click the answer and drag, or use Settings (wrench) → … Desmos shows ~4 decimals; the exam usually wants 2–4. Do not round in the middle of a calculation — keep everything in Desmos until the end.

📚 The functions

Type this	Gives you	Notes
`mean(L)`	x̄	works on a table column too: `mean(y₁)`
`median(L)`	median
`mode(L)`	mode(s)	returns a list if there is a tie
`stdev(L)`	sample SD (n − 1)	use this one for sample data
`stdevp(L)`	population SD (N)	only when L is the whole population
`var(L)`, `varp(L)`	variance	SD squared
`min(L)`, `max(L)`	smallest / largest	range = max − min
`quartile(L, k)`	k = 0 min, 1 Q1, 2 median, 3 Q3, 4 max	IQR = quartile(L,3) − quartile(L,1)
`quantile(L, 0.9)`	90th percentile	any percentile as a decimal
`total(L)`, `length(L)`	Σx and n
`histogram(L, 10)`	draws a histogram, bin width 10	zoom the graph to see it
`boxplot(L)`	draws a box plot	hover the box for the five numbers
`dotplot(L)`	draws a dot plot
`corr(x₁, y₁)`	r	needs a table
`y₁ ~ m x₁ + b`	best-fit line, prints m, b, r, r²	tilde, not equals
`normaldist(μ, σ)`	a normal curve; `.cdf(a,b)` area, `.inversecdf(p)` value, `.pdf(x)` height	blank () = standard normal
`tdist(df)`	t curve; same .cdf / .inversecdf	df = n − 1
`binomialdist(n, p)`	binomial; `.pdf(k)` exactly k, `.cdf(k)` at most k, `.cdf(a,b)` between	`.mean`, `.stdev`
`poissondist(λ)`	Poisson (counts per interval)	if your section covers it
`ttest(L, μ₀)`	one-sample t-test: statistic, p-value, CI	from raw data; `ttest(L, 30, alternative: "greater")` for one tail
`nCr(n, k)`	combinations	also `nPr`, `n!`

🧮 Recipes

📈 1. Describe a list

1L = [92, 98, 104, 104, 106, 110, 115, 126]

2mean(L), median(L), mode(L)105.6, 105, 104

3stdev(L)10.64

4max(L) − min(L)34 (range)

5quartile(L,1), quartile(L,3)Q1, Q3

6quartile(L,3) − quartile(L,1)IQR

7boxplot(L)then hover it

8histogram(L, 10)

🔢 2. z-score for one value

1(2500 − 3400) / 500= −1.8

2normaldist(3400, 500).cdf(−infty, 2500)= 0.0359 area below

🔮 3. Normal probabilities

1W = normaldist(3400, 500)

2W.cdf(−infty, 2500)less than: 0.0359

3W.cdf(2500, infty)greater than: 0.9641

4W.cdf(3000, 4000)between: 0.6731

5W.inversecdf(0.90)value at 90th percentile: 4040.8

6W.inversecdf(0.025), W.inversecdf(0.975)middle 95% cut-offs

🎲 4. Sample means (CLT)

1M = normaldist(3400, 500 / sqrt(25))SD becomes σ/√n

2M.cdf(−infty, 3200)= 0.0228

3(3200 − 3400) / (500 / sqrt(25))z = −2 by hand

🎲 5. Binomial

1B = binomialdist(10, 0.3)

2B.pdf(3)exactly 3: 0.2668

3B.cdf(3)at most 3: 0.6496

41 − B.cdf(3)at least 4: 0.3504

5B.cdf(2, 5)2 to 5 inclusive

6B.mean, B.stdev3, 1.449

📉 6. Scatter plot, r and the best-fit line

1+ → Table: x₁ = BMI, y₁ = BP

2y₁ ~ m x₁ + bDesmos prints r, r², m, b

3corr(x₁, y₁)r alone

4m · 30 + bpredict y at x = 30

📏 7. Confidence interval for a mean (t)

1t = tdist(39).inversecdf(0.975)t* = 2.0227 for 95%, n = 40

2E = t · 14 / sqrt(40)margin of error 4.477

3132 − E, 132 + E127.5, 136.5

4132 pm Esame thing, shorter

💡 For 90% use inversecdf(0.95); for 99% use inversecdf(0.995). Always (1 + confidence)/2. Known σ? Use normaldist().inversecdf(…) instead of tdist.

📏 8. Confidence interval for a proportion

1p = 120/200p̂ = 0.6

2E = 1.96 · sqrt(p(1 − p)/200)0.0679

3p pm E0.532, 0.668

⚖️ 9. Hypothesis test for a mean (t)

1t = (33.5 − 30) / (9 / sqrt(36))test statistic 2.333

2tdist(35).cdf(t, infty)right-tailed p = 0.0128

32 · tdist(35).cdf(t, infty)two-tailed p = 0.0255

4tdist(35).cdf(−infty, t)left-tailed p (if Hₐ is <)

5tdist(35).inversecdf(0.95)critical t for right-tailed α = 0.05: 1.690

⚖️ 10. Hypothesis test for a proportion (z)

1z = (62/250 − 0.20) / sqrt(0.20 · 0.80 / 250)1.897

22 · normaldist().cdf(z, infty)two-tailed p = 0.0578

🔢 11. Sample size

1(1.96 · 15 / 2)^2216.09 → round UP to 217

20.25 · (1.96 / 0.04)^2600.25 → 601 (proportion, no estimate)

📋 12. From raw data straight to a t-test

1L = [33, 28, 41, 36, 30, 39, 35, 31]eight wait times

2ttest(L, 30)t, p-value and CI in one line

3ttest(L, 30, alternative: "greater")one-tailed version

⚠️ The five Desmos mistakes that cost points

❌ stdevp instead of stdev

Sample data → stdev. Population → stdevp. They differ more for small n.

❌ Forgetting √n

Sample mean questions use normaldist(μ, σ/sqrt(n)), never plain σ.

❌ Wrong side of the curve

“More than” is cdf(x, infty). “Less than” is cdf(−infty, x). Draw it first.

❌ = instead of ~

Regression needs the tilde. With = Desmos just draws a line through nothing.

❌ Rounding early

Name intermediate results (E = …) and reuse the name. Round only the final answer.

MAT 300 · built from your own course files (the statistics study guide, the Desmos guide, the formula sheet and the final-exam study questions) with nursing examples. Not a substitute for the textbook — check any number against your own notes before an exam.