Title: Week 3 Data Lab — Numerical Summaries: Center & Spread
Course: Introduction to Statistics (18-Week Generic Edition)

Course: Introduction to Statistics (18-week generic edition) Objective: Objective 2 — numerical summaries: center, spread, five-number summaries, outliers · SLO A (reason quantitatively from data) Worth 50 points · Data labs group = 15% of the grade · Data Lab 3 · Due: end of Week 3 Format: a hands-on data lab — real research data, a spreadsheet, and a deliberate act of data sabotage; 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

Week 1 you met the penguins and drew a random sample. Week 2 you drew their pictures. This week you compress those pictures into honest numbers: the center and spread of body mass, separately for each species — mean, median, SD, five-number summary, IQR — plus the 1.5×IQR rule that formally flags outliers.

Then comes the fun part: you will sabotage your own dataset. One fat-fingered typo — a penguin entered at an impossible 9,999 grams — gets injected on purpose, and you'll watch, live, which summaries lurch (mean, SD) and which shrug (median, IQR). That's this week's biggest idea, resistance, demonstrated on real research data by you.

The data (same as Weeks 1–2): 344 penguins measured at Palmer Station, Antarctica (2007–2009) — three species, three islands, released as the freely available palmerpenguins teaching dataset.

Part 2 — The Task

The guiding question: How different are the three penguin species in body mass — in center AND in spread — and what happens to each summary when one impossible value sneaks into the data?

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 (10 min, by hand — no dataset needed). A field notebook page lists the body masses, in grams, of 10 Adélie penguins:

The table below lists one practice value per penguin (already sorted for you).

Penguin | Body mass (g)
1 | 3300
2 | 3500
3 | 3600
4 | 3700
5 | 3700
6 | 3800
7 | 3900
8 | 4000
9 | 4100
10 | 4400

By hand (calculator fine), using the class split-the-halves method for quartiles, compute and write down: the mean, median, mode, five-number summary (min, Q1, median, Q3, max), and IQR. Then compute the 1.5×IQR fences and check: are any of the 10 masses flagged? (Keep these answers — Table 2 reuses this warm-up set.)

Now the real data:

1. Import the dataset exactly as in Data Lab 1 (open the CSV link, select all, copy, paste into cell A1, then Data ▸ Split text to columns if needed; or Excel: Data ▸ From Web). Confirm the import with =COUNTA(A2:A400) → it should say 344 rows. The 8 columns are species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year.
2. Split the masses by species. Turn on Data ▸ Create a filter. Filter species to Adelie only, select the visible body_mass_g cells, copy, and paste into column J (label J1 "Adelie"). Repeat for Chinstrap into column K and Gentoo into column L. Turn the filter off. (A few cells say NA — real fieldwork has gaps; leave them, the functions below skip text automatically.)
3. Count each column: =COUNT(J2:J200), and the same for K and L — record the counts in Table 1. (=COUNT counts numbers only, so NA cells are skipped — that's what you want.)
4. Fill Table 1 using, for each species column: =MIN(), =QUARTILE(range,1), =MEDIAN(), =QUARTILE(range,3), =MAX(), the IQR by subtraction, =AVERAGE(), and =STDEV(). (Convention note: =QUARTILE interpolates, so it can differ a bit from the hand method — on the warm-up set it gives Q1 = 3625 and Q3 = 3975 where the hand method gives 3600 and 4000. Neither is wrong; in Table 1, use =QUARTILE and say so.)
5. Run the outlier rule on Adelie. From Table 1's Adelie row: compute 1.5 × IQR, then the fences Q1 − 1.5·IQR and Q3 + 1.5·IQR. Compare with the Adelie min and max: is any Adelie mass flagged? Record the fences and the verdict.
6. Sabotage. In your Adelie column, find the first value — it's 3750 (the very first penguin in the file) — and retype it as 9999 (a data-entry typo: a smudged 3 read as a 9). Watch =AVERAGE(), =MEDIAN(), and =STDEV() update live. Record the before/after values in Table 2, and check the new maximum against your fences from step 5.
7. Undo the sabotage (retype 3750) so your Table 1 stays honest — and note what just happened: the rule that found nothing suspicious in the real data instantly flagged the typo.
8. Verify the shift arithmetic. Replacing one value x with y in a column of n numbers moves the mean by exactly (y − x) ÷ n. For your Adelie column: (9999 − 3750) ÷ your Adelie count. Check that your observed mean jump matches (small rounding aside) — this is the graded arithmetic.

Fallback (no import available): do everything with printed data instead. Use the 10-penguin warm-up table as your "Adelie" column, and this second sorted set as your "Gentoo" column (grams): 4600, 4800, 4900, 5000, 5000, 5200, 5400, 5500 — hand stats: mean = 5050, median = 5000, Q1 = 4850, Q3 = 5300, IQR = 450 (technology gives SD ≈ 302). Run the sabotage on the warm-up set by adding an 11th value, 9,905 g: the mean jumps from 3,800 to exactly 4,355 while the median moves only from 3,750 to 3,800. State in your submission that you used the fallback.

Part 4 — The Scaffold (complete both tables)

Table 1 captures each species' body-mass summary from your own import (record =QUARTILE values for Q1/Q3).

Species | Count (=COUNT) | Min | Q1 | Median | Q3 | Max | IQR | Mean | SD (=STDEV)
Adelie | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______
Chinstrap | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______
Gentoo | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______

Table 2 captures the sabotage experiment on your Adelie column (steps 6–8), plus the fence check.

Quantity | Before (real data) | After (3750 → 9999)
Adelie mean (g) | ______ | ______
Adelie median (g) | ______ | ______
Adelie SD (g) | ______ | ______
Largest value vs. upper fence — flagged? | ______ | ______
Observed mean jump vs. (9999 − 3750) ÷ count | — | ______

Part 5 — Analysis Questions

Answer in 1–3 sentences each:

1. Rank the three species by typical body mass using your medians. For each species, compare its mean to its median — does any species show the mean sitting noticeably above the median, and what would that suggest about the shape (Week 2 vocabulary welcome)?
2. Using Table 2 and the word resistant, explain what the sabotage demonstrated: why did the mean and SD lurch while the median barely moved (or didn't move at all)?
3. Before the sabotage, the 1.5×IQR rule likely flagged nothing in your Adelie column. Is "no outliers" a failure of the rule? What does its instant reaction to the 9,999 g typo show about what the rule is for?
4. Error sources: name one way a number in your Table 1 could be wrong even though the spreadsheet "computed it correctly" — e.g., what would using =STDEVP() instead of =STDEV() do, or what happens if a filter accidentally leaks another species into a column, or the NA cells get typed over? Pick one and explain the damage in a sentence.
5. Looking ahead: you just summarized one quantitative variable (mass) separately across the values of one categorical variable (species). What does comparing the three medians tell you that a single all-344-penguin median would hide? (Next week this side-by-side idea becomes the study of relationships between two variables.)

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 and Table 2 into your chatbot and ask: "Check my summary statistics for internal consistency. Then tell me: is the jump in the Adelie mean after one value was retyped to 9,999 an error in my spreadsheet?"
2. Check everything it says against your own work: - Did it recompute your SD with the wrong divisor? (Chatbots routinely divide by n instead of n − 1 — the =STDEVP() mistake in prose form — and then "correct" your right answer.) - Did it call the sabotage jump a calculation error? (It isn't — it's the non-resistance of the mean, doing exactly what the math says: the jump is (9999 − 3750) ÷ count.) - Did it "fix" your quartiles to different values? (Different quartile conventions disagree slightly — that's not an error either.) - Did it accept a 9,999 g penguin as plausible? (No penguin weighs 10 kilograms — a real analyst questions the value, not just the arithmetic.)
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 use the wrong divisor or "correct" a right quartile — catching it is the point.

Part 7 — What to Submit

One document or text entry containing: your warm-up hand computations (mean, median, mode, five-number summary, IQR, fences, flag verdict), 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 3 · 50 points (rubric below the key).

Grading rubric — 50 points

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

Criterion | Full | Partial | None
Warm-up hand computations — mean 3,800; median 3,750; mode 3,700; five-number 3300/3600/3750/4000/4400; IQR 400; fences 3,000/4,600; "no flags" (5) | 5 | 3 | 0–1
Import + species columns + Table 1 — counts 151/68/123; all cells computed with the named functions; values inside sanity rails or method-defended (15) | 15 | 8–12 | 0–6
Outlier rule on Adelie — fences computed from their own Q1/Q3; correct comparison and verdict (8) | 8 | 4–6 | 0–3
Sabotage experiment (Table 2) — before/after recorded; mean-jump matches (9999 − 3750) ÷ count; median/SD behavior noted; fence flag caught (8) | 8 | 4–6 | 0–3
Analysis questions — Q1–Q5 hit the expected ideas, especially resistance in Q2 and the rule's purpose in Q3 (9) | 9 | 5–7 | 0–4
AI-critique — specific catch or verification reported in 2–3 sentences (5) | 5 | 3 | 0–2