Week 3 Data Lab: Center, Spread, and Fences for 342 Penguins

Part 1 — The Big Picture

This week you learned to name the middle of a dataset three ways, to read skew from the gap between the mean and the median, to measure spread with a standard deviation that divides by one less than the sample size, and to sum up a whole variable with five numbers and two fences. In this lab you open the real penguin field log yourself, compute every one of those summaries for 342 body masses with spreadsheet formulas, draw or sketch the boxplot, check the 1.5 × IQR rule against the lightest and heaviest birds, and compare the spread of the three species. Then you check a chatbot's summary of the same data.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: What is a typical body mass for the penguins in the field log, how far do the masses stray from it, and does any penguin sit far enough out to flag?

Workshop data: palmer-station-penguins

Get the data: palmer-station-penguins landing page or the direct data file — free, no login required.

Source: Measurements of 344 penguins of three species on three islands of Antarctica's Palmer Archipelago, recorded by field researchers and republished in the palmerpenguins package.

• Rows: 344 penguins
• Columns: species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year
• Missing values: Numeric measurement columns and sex carry missing values for a small number of penguins

Part 3 — Materials & Procedure

Tools and materials

• Google Sheets (free) or Excel
• The palmerpenguins CSV file
• A document or notebook for your written answers

Ways of working

• interpret-real-data
• compute-and-plot
• structured-observation

Procedure

1. Open a blank sheet. In Google Sheets, click cell A1 and type =IMPORTDATA("https://raw.githubusercontent.com/allisonhorst/palmerpenguins/main/inst/extdata/penguins.csv"). In Excel, save the file from that address, then use Data, then From Text/CSV, and load it starting in cell A1. Tool: Google Sheets (free) or Excel. Check: Row 1 shows the eight column names, the penguins fill rows 2 through 345, and body mass is column F.
2. In empty cells, type =COUNT(F2:F345), =AVERAGE(F2:F345), =MEDIAN(F2:F345), and =STDEV.S(F2:F345). Format the mean and the standard deviation to two decimals, and record all four in the first scaffold table. The two NA entries are text, so every formula skips them. Tool: Google Sheets (free) or Excel. Check: The count is 342, the median is a whole number of grams, and the mean sits above the median.
3. For the five-number summary, type =MIN(F2:F345), =QUARTILE.INC(F2:F345,1), =MEDIAN(F2:F345), =QUARTILE.INC(F2:F345,3), and =MAX(F2:F345). Then compute the IQR as the third quartile minus the first, the step as 1.5 times the IQR, the lower fence as Q1 minus the step, and the upper fence as Q3 plus the step. Record everything in the second scaffold table. Tool: Google Sheets (free) or Excel. Check: The five numbers rise from left to right, the lightest bird is 2,700 g and the heaviest is 6,300 g, and the IQR is a positive number of grams.
4. Count the flagged penguins on each side: =COUNTIF(F2:F345,"<"&L5) and =COUNTIF(F2:F345,">"&L6), replacing L5 and L6 with the cells that hold your lower and upper fences. Record both counts. Tool: Google Sheets (free) or Excel. Check: Each formula returns a whole number; compare it with your minimum and maximum to confirm it.
5. Draw the boxplot. In Excel, select F1:F345 and use Insert, then Insert Statistic Chart, then Box and Whisker; right-click the box, choose Format Data Series, and set Quartile Calculation to Inclusive median. Google Sheets has no one-click boxplot, so sketch it on paper from your five numbers on a gram scale, with dashed lines at the two fences. Tool: Google Sheets (free) or Excel. Check: A box from Q1 to Q3 with a line at the median and a whisker on each side, plus two marked fences.
6. Compare the species. For each species, type =AVERAGEIF(A2:A345,"Adelie",F2:F345) and =STDEV.S(FILTER(F2:F345,A2:A345="Adelie")), then change the name to Chinstrap and Gentoo, and record the six values in the third scaffold table. If FILTER is not available in your Excel version, use the fallback model data for this table. Tool: Google Sheets (free) or Excel. Check: Three means and three sample standard deviations, each in grams; the Gentoo mean is the largest.
7. Answer the analysis questions in your document, then paste your tables into an approved chatbot with the prompt in Part 6 and check its answer against the scripted checks. Tool: A document or notebook for your written answers. Check: You have five written answers and a list of the chatbot's errors with corrections.

Fallback route

When to use it: Use this route if the file will not import or no spreadsheet is available.

Work from the model data below, which reports the summaries from the real file. Complete all three scaffold tables, compute the IQR and the fences by hand, sketch the boxplot on paper with the fences marked, and answer every analysis question and the critique step from them; submit the same items for equal credit.

This route earns the same credit as the primary route.

These summaries of the real file give you every value the lab needs without importing it.

Fallback model data

Quantity from the file	Value
Recorded body masses	342
Mean and median of the body masses	4,201.75 g and 4,050 g
Sample standard deviation of the body masses	801.95 g
Minimum, Q1, median, Q3, maximum	2,700, 3,550, 4,050, 4,750, and 6,300 g
Adelie mean and sample standard deviation	3,700.66 g and 458.57 g
Chinstrap mean and sample standard deviation	3,733.09 g and 384.34 g
Gentoo mean and sample standard deviation	5,076.02 g and 504.12 g
IQR and the two fences of the 1.5 × IQR rule

Part 4 — The Scaffold

Record the center and spread of all 342 body masses, so you can compare the mean with the median and read the typical distance from the mean.

Student scaffold table 1

Quantity	Formula you used	Your value
Number of recorded body masses (n)
Mean, x̄ (g)
Median (g)
Mean minus median (g)
Sample standard deviation, s (g)

Build the five-number summary and the fences, so you can apply the 1.5 × IQR rule with evidence.

Student scaffold table 2

Quantity	Your value (g)
Minimum
Q1
Median
Q3
Maximum
IQR = Q3 − Q1
Step = 1.5 × IQR
Lower fence = Q1 − step
Upper fence = Q3 + step
Penguins below the lower fence
Penguins above the upper fence

Compare the center and spread of the three species, so you can see how mixing groups affects the spread of the whole file.

Student scaffold table 3

Species	Mean body mass (g)	Sample standard deviation (g)
Adelie
Chinstrap
Gentoo

Part 5 — Analysis Questions

1. Using your second table, show the steps from Q1 and Q3 to the IQR, the step, and both fences. Then say whether the 1.5 × IQR rule flags any penguin, and use your minimum and maximum to explain why.
2. Compare the mean with the median and describe your boxplot in words: where the median line sits inside the box and which whisker is longer. Name the shape of body mass by its tail, and give both pieces of evidence.
3. Explain why the formula for the 342 masses is STDEV.S, which divides by one less than the count, rather than STDEV.P. Then say what units the variance of body mass would be in, and why you report the standard deviation instead.
4. From your third table, which species has the largest standard deviation, and which has the smallest? The standard deviation of all 342 masses together is larger than any one species' standard deviation; explain in plain words why mixing three species with different typical masses spreads the values out.
5. Choose one and answer it in 3–4 sentences. (a) Another common quartile method puts Q3 at 4,756.25 g instead of 4,750 g: recompute the upper fence with that value and say whether any verdict changes, and what that tells you about trusting one tool's quartiles. (b) Two penguins in the file have no measurements at all: how could leaving them out, or a typing error in one recorded mass, change the mean, the median, and the standard deviation, and which of the three would you trust most?

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 3 Data Lab tables above. They come from the Palmer penguins file, which has 344 rows and 8 columns: species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, and year; 342 penguins have a recorded body mass. Please do five things. First, give the mean, the median, the sample standard deviation, and the five-number summary of body mass, and say whether the 1.5 x IQR rule flags any penguin. Second, say which way body mass is skewed and how you can tell from the mean and the median. Third, say whether these data show that living on Biscoe makes penguins heavier. Fourth, as a stretch question for later in the course, say what the chance is that exactly one of two penguins picked at random weighs more than the median. Fifth, also as a stretch question, say how sure we can be about the average body mass of all penguins in the archipelago.

Test the response for these likely failures:

• Chatbots often report summary numbers they never computed, such as a round mean of 4,200 g, a standard deviation of 800 g, or quartiles of 3,500 g and 4,800 g, or they divide by the full count and give a population standard deviation for a sample.
• Chatbots often say body mass is left-skewed because most penguins sit at the lighter end, or claim the mean below the median signals a right skew, getting the direction backwards.
• Chatbots often slide from a pattern to a cause, saying Biscoe's conditions make penguins heavier because the heavy Gentoo penguins were all logged there.
• On the stretch chance question, chatbots often multiply the chance of a heavier-than-median penguin by the chance of a lighter one once and stop, forgetting that the heavier penguin could be the first pick or the second.
• Asked how sure we can be, chatbots often invent an interval and say there is a 95% chance the true average is inside it, or that 95% of penguins weigh an amount inside it.

Write 3–5 sentences naming one thing the chatbot got right and at least two places it went wrong or overreached, quoting its words and correcting each with evidence from your own tables, your boxplot, or the field log.

Equivalent route (no AI required)

No AI account is required for this lab. Instead of the chatbot, critique this flawed analysis, printed here in full: "The penguins' average body mass is 4,200 g, the median is 4,100 g, and the standard deviation is 800 g, worked out by dividing by all 342 birds. Because most penguins are on the lighter side, body mass is left-skewed. The quartiles are 3,500 g and 4,800 g, so a 6,300 g penguin is an outlier and should be removed. Living on Biscoe makes penguins heavier, since the heaviest species lives there. The chance that exactly one of two random penguins is heavier than the median is one half times one half, and nothing more. We can be 95% sure that 95% of all penguins weigh between 3,400 g and 5,000 g." Mark it up: quote each flawed sentence, name what is wrong (an invented statistic, the wrong divisor, a flipped skew direction, a deleted flagged value, cause read from association, a dropped number of ways, or a misread confidence statement), cite the evidence from your tables, boxplot, or the field log, and write a corrected sentence beneath it; for the last two sentences, say what the course will check later. This route assesses the same objective (Objective 2 — summarize and display a single quantitative or categorical variable with appropriate tables and graphs, and describe its distribution's shape, center, and spread with the right numerical summaries) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All three completed scaffold tables
• Your boxplot or a labelled sketch of it, with both fences marked
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Data Lab report on the real Palmer penguins field log: three completed tables (center and spread of the 342 body masses, the five-number summary with the IQR and both fences, and the mean and sample standard deviation of each species), a boxplot or a labelled sketch of it with the fences marked, written answers to five analysis questions, and a critique of a chatbot's summary of the same data, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Computing center and spread	The file is opened or the fallback model data is used, and the count, mean, median, mean-minus-median gap, and sample standard deviation are recorded with the formula or step behind each, with the standard deviation dividing by one less than the count.	The summaries are present, but one or two are missing or wrong, or the population version of the standard deviation is used for the sample.	No summaries are recorded, or they are invented rather than computed.
Five numbers, fences, and the boxplot	The five-number summary, the IQR, the step, and both fences are correct and follow from Q1 and Q3 with the steps shown, the flagged counts are checked against the minimum and maximum, and the boxplot or sketch shows the box, the median line, both whiskers, and both fences, labelled in words.	The five numbers or the boxplot are present, but a fence is wrong or missing, the steps are not shown, or the boxplot omits a labelled part.	No five-number summary, fences, or boxplot, and no sketch, is submitted.
Reading shape and comparing groups	Analysis questions 1 to 4 are answered accurately: the fence verdict is explained from the extremes, the shape is named right-skewed by its tail with the mean-median gap and the whiskers as evidence, the choice of STDEV.S and the squared units of variance are explained, and the species comparison and the mixed-group spread are explained in plain words.	The questions are attempted, but one or two answers name the skew by the pile, confuse the sample and population formulas, give variance the data's units, or leave out a reason.	The analysis questions are missing or do not address the penguin data.
Critique of the chatbot or of the printed flawed analysis	On either route, at least two errors are quoted and corrected with evidence from the student's own tables, boxplot, or the field log, and one correct point is acknowledged; both routes earn this band equally.	On either route, errors are named but corrected without evidence, or only one error is caught.	No critique appears, or pasted output is submitted without any checking.
Reflection on how far to trust a summary	The chosen reflection option is answered in 3–4 sentences that connect a specific issue, the quartile method or a missing or mistyped value, to which summaries change and which can be trusted.	The reflection is answered but stays general or does not connect the issue to a specific summary.	No reflection is submitted.

Quality Gate

• Every value in the tables comes from your own formulas or the fallback model data, never from memory or a chatbot.
• The five-number summary rises from minimum to maximum, and the IQR, the step, and both fences follow from Q1 and Q3 with the steps shown.
• The standard deviation is the sample version that divides by one less than the count, and it is reported in grams.
• The shape of body mass is named by the direction of its tail, with the mean, the median, and the boxplot as evidence.
• No statistic, count, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence from your tables or boxplot.