What statistics really is, and the kinds of data we'll work with all semester.
Statistics has a scary reputation, but here's the secret — it's really about thinking and deciding, and the math is just a little 8th-grade arithmetic. This first unit is about getting comfortable: what stats is (and isn't), the words you'll hear all semester, and the one dataset we'll use every week. By the end you'll have it open and running — and you'll never again do math on a column without first asking what kind of number am I holding?
Statistics is not a branch of pure math.
It uses math, yes — but its real job is to take a messy pile of numbers and help you think clearly and decide something. "Do students who sleep more get better grades?" That's a stats question, and the arithmetic is the easy part. If math has scared you off before, take a breath: the hard part here is the thinking, and you already do that every day.
Here's the shape of it: every statistical question is really a decision under uncertainty. You have data (raw numbers), you turn it into information (a summary, a comparison, a pattern), and you use that to make a decision or a claim. Nearly every finding you'll read in psychology — "therapy reduces anxiety," "sleep predicts GPA," "this drug beats placebo" — is exactly this move: numbers from a small group, turned into a careful claim about a bigger one.
Statistics does two big jobs:
| Type | Plain English | What it answers | Example |
|---|---|---|---|
| Descriptive | Summarize the data you have | "What does this group look like?" | "Our 200 students sleep 6.8 hours on average." |
| Inferential | Generalize beyond the data | "What's true of the bigger group?" | "Students in general probably sleep about 7." |
Most of Block 1 is descriptive — describing the group in front of us with averages, spreads, and pictures. Later in the course we move to inferential, where we use a small group to make a smart, hedged guess about a much bigger one. Same data, two very different jobs.
A population is everyone you care about — say, all students at the university. A sample is the smaller group you actually measured — like our 200 students. Two more words travel with these:
Why bother with a sample at all? Because measuring the whole population is usually impossible, too slow, or too expensive — and sometimes the population is hypothetical (all future patients who might take a drug). So we measure a manageable slice instead. The catch: a sample is only useful if it's representative — if it resembles the population in the ways that matter. A biased sample (say, only students who volunteer for an 8 a.m. study) can mislead you no matter how large it is. Bigger is not the same as fairer.
One tiny wrinkle to expect every time: a sample statistic won't exactly equal the population parameter — that gap is sampling error, and taming it is what the whole back half of the course is about.
There's a handy convention: numbers about a population usually wear Greek letters — μ (mu) for its mean, σ (sigma) for its standard deviation. Numbers about a sample wear Latin ones — x̄ ("x-bar") for its mean, s for its standard deviation. Quick mnemonic: Greek = population/parameter, Latin = sample/statistic.
We almost never get the whole population, so we work with a sample and a statistic, then use inferential stats to make a smart guess about the parameter. That's it — that's the entire arc of the course.
A variable is just a thing that varies from person to person — like gender, sleep, or GPA. (If it doesn't vary — say everyone in your study is a sophomore — then for your study it's a constant, not a variable.) Variables come in two flavors:
| Type | What it does | In our dataset |
|---|---|---|
| Categorical (qualitative) | Puts people in groups — the value is a label, not a quantity | gender (B), commuter (D) |
| Quantitative | An actual number you can do math on | sleep_hours (F), gpa (K) |
Quantitative numbers come in two styles:
words_recalled in column R). You can't recall 7.5 words.commute_minutes in column W, sleep_hours). The only limit is how precisely your instrument measures.One subtlety worth knowing: the same real-world thing can be measured either way. "Caffeine" could be a category (coffee drinker vs not) or a quantity (mg per day). How you measure it — not the thing itself — decides the type, and that decision controls every statistic that follows.
sleep_hours, which can be 6.8 (continuous).This is the big one. Every variable sits on one of four scales, and the scale decides which statistics you're allowed to use. They build on each other, from least to most information:
| Scale | What it is | In our dataset |
|---|---|---|
| Nominal | Unordered categories — just names | gender (B), commuter (D), pay_condition (O) |
| Ordinal | Categories with an order, but uneven gaps | class_year (C), processing_level (Q) |
| Interval | Numbers, equal gaps, but no true zero | scale scores: stress (J), wellbeing (M), self_compassion (N) |
| Ratio | Numbers with a true zero (zero means none) | sleep_hours (F), gpa (K), commute_minutes (W) |
The reason this matters so much is that the scale sets a menu of moves you're allowed to make. Each step up the ladder unlocks more:
| Scale | You can… | Center you may report |
|---|---|---|
| Nominal | count, compare frequencies, find the most common category | Mode |
| Ordinal | …also rank and find the middle position | Median (+ mode) |
| Interval | …also add/subtract and average; differences are meaningful | Mean (+ median, mode) |
| Ratio | …also form true ratios ("twice as much") because zero is real | Mean + ratios/CV |
Is there a true zero? With commute_minutes, 0 means no commute at all — and 40 minutes is truly twice 20. That's ratio. With a stress scale, a 0 doesn't mean "no stress exists," and a 30 isn't literally "twice as stressed" as a 15 — the gaps are equal but the zero is fake. That's interval.
The classic interval trap is temperature. 20°C is not "twice as hot" as 10°C, because 0°C doesn't mean "no temperature" — it's just where someone decided to put the zero. Equal gaps (each degree is the same size), fake zero → interval. Height and weight, by contrast, have real zeros, so they're ratio: 100 kg really is twice 50 kg.
commute_minutes interval or ratio?Why it matters: you can find the most common gender (a mode), but you can't take its average — there's no "mean gender." Scale first, statistic second. We'll lean on this all semester.
Don't panic. Here's everything you'll actually need — and it really is just middle-school arithmetic dressed up in Greek letters.
Order of operations (PEMDAS): Parentheses, Exponents, Multiply/Divide, Add/Subtract. So 2 + 3 × 4 = 14, not 20 — the × happens first.
Negative numbers: subtracting a bigger number gives a negative. 5 − 8 = −3. Two negatives multiplied turn positive: −2 × −2 = 4.
Rounding to 2 decimals: look at the 3rd decimal. 3.146 → 3.15; 3.142 → 3.14. Round at the end, not mid-calculation.
Squaring & square roots: squaring means times-itself — 4² = 16. A square root undoes it — √16 = 4. In Sheets that's =SQRT(16).
Summation Σ: that big Greek letter just says "add them all up." Σx = add up all the x's. Nothing more.
Σ shows up constantly because almost every formula starts by adding things together. The very first one you'll meet is the mean (the average), and it's just two of these tools stacked:
mean = x̄ = Σx ÷ n — add up all the values (Σx), then divide by how many there are (n). That's the entire thing. Try it below.
Type a few numbers. The calculator shows the count (n), the sum (Σx), and the mean — and spells out exactly how they connect.
We do everything in Sheets, in the lab. Four things to know:
J2 (column J, row 2).J2:J201 (all 200 students' stress scores).=. Type a formula and Sheets does the math for you.In our dataset the data lives in rows 2–201 (row 1 is the column headings), so a full column of data is always 2:201. A handful of functions will carry you through Block 1:
=AVERAGE(F2:F201) → the mean of all 200 sleep_hours values
=SUM(G2:G201) → Σx: adds a whole column
=COUNT(F2:F201) → n: how many numbers are in the range
=COUNTIF(C2:C201,"Senior") → counts how many Seniors (categorical!)
=SQRT(16) → 4 (Sheets does square roots too)Notice the payoff of Unit 1's big lesson right here: AVERAGE and SUM only make sense on quantitative columns. Point them at gender and you'll get nonsense — for a categorical column you reach for COUNTIF instead. The scale you decided on tells you which formula is even legal.
commuter = "Yes"/"No"). Which formula fits?commuter is categorical (nominal), so averaging is meaningless — there's no "mean Yes/No." You count categories. AVERAGE is for quantitative columns like sleep_hours.Here's a number to keep in your back pocket all semester: roughly 83 billion land animals are farmed for food each year — about 2,600 every second, and around 90% of them are chickens. That's a count of a categorical variable (species), which means the right summary is a frequency or a percentage, never an "average species."
One more figure shows why the kind of number matters: meat and dairy use 83% of the world's farmland but provide only 18% of our calories (Poore & Nemecek, 2018). Those are percentages — ratio-scale numbers with a true zero — so they're fair to compare directly. The skill this whole unit is building is exactly that: before you do any math, ask what kind of number you're holding. We'll graph and argue about data like this all term, because statistics is most worth learning when the numbers are about something that matters.
Your ZIP code is written with digits. So is your phone number and a player's jersey number. But try to find the average ZIP code of your class — it's nonsense. ZIP 10301 isn't "more" than 07024, and the average of two phone numbers doesn't call anyone.
The lesson: these are nominal labels that just happen to be printed as digits. Before you do any math on a column, ask "is this a real number, or just a label in disguise?" That single question saves you from a lot of nonsense.
Digits ≠ quantity — ZIP codes, IDs, and pay-condition codes are categories even when they look numeric. There's no true zero on interval scales, so you can't say one stress score is "twice" another. You can't average a category (no "mean gender") — use a count or the most-common value. Round at the end, and remember every formula needs the = or Sheets just shows your text.
Ten quick true/false items with instant explanations. (Different from your Canvas quiz — real practice.)