← Back to the Introduction to Statistics outline The Course Maker
← Introduction to Statistics outline
Week 1 · Data Lab

Week 1 — Data Lab · "Meet Your Data: The Penguins of Palmer Station"

Introduction to Statistics Generic evergreen edition

Course: Introduction to Statistics (18-week generic edition)
Objective: Objective 1 — populations vs. samples; variable types; sampling · SLO A (reason quantitatively from data)
Worth 50 points · Data labs group = 15% of the grade · Data Lab 1 · Due: end of Week 1
Format: a hands-on data lab — real research data, a spreadsheet, and your own randomly drawn sample; then you catch the AI's mistakes when it interprets your work.

This is the course's signature weekly component. Every instructional week has a Data Lab: real, free, linked public data — nothing to buy, download from a store, or sign up for — worked in your spreadsheet, finished with an AI-critique step. Plan on 60–90 minutes.

Part 1 — The Big Picture

This week you learned that every trustworthy statistic starts with two questions: who was measured, and what was recorded? Today you'll answer those questions about a real scientific dataset — and then experience, hands-on, the single most important phenomenon in this course: two honest samples from the same data give two different answers. (That idea, sampling variability, becomes the engine of everything after the midterm.)

The data: between 2007 and 2009, researchers at Palmer Station, Antarctica measured 344 penguins from three species (Adélie, Chinstrap, Gentoo) across three islands — bill and flipper dimensions, body mass, and sex. The data were released as the freely available palmerpenguins teaching dataset. It's real field science, small enough to see whole, and perfect for Week 1.

Part 2 — The Task

The guiding question: What did these researchers actually measure — and when you draw your own random sample from their data, how close does your sample's answer land to the full dataset's answer?

The dataset (both links are free, no login):
- About the data — palmerpenguins documentation
🔗 https://allisonhorst.github.io/palmerpenguins/
- The data itself (CSV file, opens as plain text)
🔗 https://raw.githubusercontent.com/allisonhorst/palmerpenguins/main/inst/extdata/penguins.csv

Part 3 — Materials & Procedure

You need: a web browser and a spreadsheet — Google Sheets (free) or Excel. Nothing else.

Warm-up (5 min, no dataset needed). Here are the body masses, in grams, of 10 penguins. Compute their mean by hand or with a calculator before you open the spreadsheet — you'll use this to check your spreadsheet skills in a moment.

The table below lists one practice value per penguin.

Penguin Body mass (g)
1 3700
2 3900
3 4100
4 4300
5 3500
6 4700
7 3800
8 4200
9 3600
10 4200

Mean = (sum of the 10 values) ÷ 10. Write your answer down.

Now the real data:

  1. Import the dataset. In Google Sheets: open a blank sheet → File ▸ Import ▸ Upload isn't needed — instead use File ▸ Import ▸ Paste a URL? If your Sheets version has no URL import, the simplest route works everywhere: open the CSV link above in your browser, select all (Ctrl/Cmd-A), copy, paste into cell A1, then Data ▸ Split text to columns if needed. In Excel: Data ▸ From Web, paste the CSV URL. Either way you should end with 8 columns of penguin data plus a header row.
  2. Count your rows. In an empty cell, =COUNTA(A2:A400) counts the data rows. Record the number — it should be 344. If it isn't, your import dropped rows; re-import before continuing.
  3. Walk the columns. The 8 variables are: species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year. Fill in the classification table in Part 4.
  4. Look for holes. Scroll (or filter) and notice that a few cells say NA — real fieldwork has gaps. Count how many rows have NA for sex (filtering the column is the easy way). Record the count your sheet finds.
  5. Compute the full-data mean body mass. In an empty cell: =AVERAGE(F2:F345) (adjust if your data starts elsewhere). Spreadsheets skip NA/blank cells automatically. Record it.
  6. Draw YOUR simple random sample of 20. In the first empty column, row 2, type =RAND() and fill down beside every penguin. Select your whole data range → Data ▸ Sort range by the RAND column. The top 20 rows are your SRS. (Re-sorting reshuffles — that's the randomness working.)
  7. Compute your sample's mean body mass — =AVERAGE(...) over just your 20 sampled rows' body-mass cells (copy the 20 rows to a scratch area if that's easier). Record it.
  8. Compare. Fill in the sampling table in Part 4: full-data mean, your sample mean, and the difference.

Fallback (no import available): if you can't get the CSV into a spreadsheet, do everything with the 10-penguin warm-up table instead — classify the two variables it shows (penguin number, body mass), compute its mean, and use rows 1–5 as your "sample." State in your submission that you used the fallback.

Part 4 — The Scaffold (complete both tables)

Table 1 lists each variable for you to classify by level of measurement, with a one-line reason.

Variable Level (nominal / ordinal / interval / ratio) Your one-line reason
species ______ ______
island ______ ______
bill_length_mm ______ ______
bill_depth_mm ______ ______
flipper_length_mm ______ ______
body_mass_g ______ ______
sex ______ ______
year ______ ______

Table 2 captures your sampling results.

Quantity Value
Rows of data (from =COUNTA) ______
Rows with NA for sex ______
Full-data mean body mass (g) ______
YOUR 20-penguin sample mean (g) ______
Difference (sample − full) ______

Part 5 — Analysis Questions

Answer in 1–3 sentences each:

  1. Who are the individuals in this dataset, and is the set of 344 a population or a sample? (Careful — it's a role, not a size. A population of what? A sample of what?)
  2. Defend your classification of year: why isn't it ratio, even though it's a number you could subtract?
  3. Your sample mean didn't exactly equal the full-data mean (almost certainly). Is that an error? What is this phenomenon called, and why does it matter for every poll you'll ever read?
  4. Compare answers with a classmate (or draw a second sample yourself): the two sample means differ from each other, too. If a news story reported your sample's mean as "the average penguin mass," what caution would you give a reader?
  5. The sex column has some NA values — penguins the team couldn't sex in the field. Which Week-1 bias concept is this most like, and what should an honest analyst do about it (at minimum, say what you'd report)?

Part 6 — AI-Critique Moment (required — the BYOAI step)

Now bring in your chatbot and be the analyst who checks its work.

  1. Paste your completed Table 1 (the classifications) and Table 2 (the numbers) into your chatbot and ask: "Check my level-of-measurement classifications and my arithmetic. Then tell me: is the difference between my sample mean and the full-data mean a mistake?"
  2. Check everything it says against your own work:
    - Did it try to "correct" a right answer? (Chatbots often call year ratio — it's interval here — or wave species into "ordinal.")
    - Did it recompute your difference correctly? (Redo the subtraction yourself.)
    - Did it explain the sample-vs-full gap as sampling variability — or did it call your work an "error" that needs fixing?
  3. Write 2–3 sentences reporting what the AI got right and at least one thing you had to correct, question, or verify. If it happened to get everything right, say how you verified each claim — that's the skill.

The habit all term: the tool drafts, you judge. A chatbot will confidently mis-add a column or misclassify a variable — catching it is the point.

Part 7 — What to Submit

One document or text entry containing: your warm-up mean, your completed Table 1 and Table 2, your Part 5 answers (1–5), and your Part 6 AI-critique paragraph. Due at the end of Week 1 · 50 points (rubric below the key).

Instructor answer key & model values — REMOVE BEFORE PUBLISHING TO STUDENTS

Students draw their own random samples, so sample means and NA counts are graded on method and interpretation, not on matching one number. Everything asserted below is pre-computed or verified against the linked source.

Warm-up mean (fixed — every student should match): (3700 + 3900 + 4100 + 4300 + 3500 + 4700 + 3800 + 4200 + 3600 + 4200) = 40,000; 40,000 ÷ 10 = 4,000 g exactly. ✓ (independently re-verified)

Dataset facts (verified against the linked CSV): 8 columns with headers exactly species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year; 344 data rows; first data row is an Adélie penguin from Torgersen Island (bill 39.1 mm, mass 3750 g, male, year 2007).

Table 1 expected classifications:

Variable Level Reason
species Nominal Three names, no order
island Nominal Place names, no order
bill_length_mm Ratio True zero; 40 mm is twice 20 mm
bill_depth_mm Ratio Same reasoning
flipper_length_mm Ratio Same reasoning
body_mass_g Ratio 0 g means none; ratios meaningful
sex Nominal Category labels
year Interval Ordered, equal gaps, but year zero is an arbitrary marker — "twice year 1004" is meaningless. (Accept a thoughtful "ratio if re-coded as years-since-study-start" note as bonus insight, not required.)

Table 2 grading: COUNTA = 344 (fixed). NA-for-sex count: grade that the student filtered and counted and reported a specific small number — spot-check one import yourself in adoption week rather than trusting any printed value here. Full-data mean: all correct imports agree with each other — check the student's value against one import of your own (a correct value is a four-digit number of grams; flag any student value wildly off from the class consensus). Sample mean: any value near the full-data mean is expected; the difference must be computed correctly from their own two numbers (re-do their subtraction — this is the arithmetic actually graded).

Part 5 expected answers:
1. Individuals = individual penguins (one row each). The 344 form a sample of the species' populations around Palmer Station (and could be treated as the population of penguins measured in this study for internal questions) — full credit requires the "role, not size" insight, with both framings acceptable if defended.
2. year is interval: ordered, equal one-year gaps, but the zero point is an arbitrary calendar marker, so ratios of years are meaningless.
3. Not an error — sampling variability: different honest samples give different statistics. It matters because every poll's number is one sample's answer, not the parameter itself.
4. Any caution naming that a single sample's mean is an estimate that would change with a different sample — e.g., "another random 20 penguins would give a somewhat different average, so don't read 4 digits of precision from 20 birds."
5. Most like nonresponse / undercoverage (some individuals couldn't be "asked"); an honest analyst reports the missing count and how it was handled (e.g., "11 penguins excluded from sex-based summaries" — accept any specific, transparent treatment; the number itself comes from their own filter).

AI-critique full credit: names a specific claim checked or corrected — most commonly the chatbot misclassifying year (calls it ratio), second-guessing a correct nominal call, or mangling the subtraction — OR documents verification of each claim. Zero credit for "the AI agreed with everything" with no evidence of checking.

Grading rubric — 50 points

The rubric below maps each part to its points; bands are full / partial / none.

Criterion Full Partial None
Warm-up + import — warm-up mean = 4,000 g; 344 rows confirmed (5) 5 3 0–1
Classification table — all 8 levels correct with sound one-line reasons (15) 15 8–12 (1–2 misses) 0–6
SRS + computations — =RAND() sort done as specified; both means computed; difference correct from their own numbers (10) 10 5–8 0–4
Analysis questions — Q1–Q5 hit the expected ideas, especially sampling variability in Q3–Q4 (15) 15 8–12 0–6
AI-critique — specific catch or verification reported in 2–3 sentences (5) 5 3 0–2

Quality gate (self-checked): warm-up arithmetic re-verified (sum 40,000; mean 4,000); dataset links live and free (documentation page + raw CSV both load without login); column names and row count verified against the fetched CSV; no numeric claim in the key depends on an unverified dataset-wide value; no graded-item leakage (no quiz/exam item uses the penguins data); rubric sums 5 + 15 + 10 + 15 + 5 = 50. ✓