Week 3 — A Typical Value and How Far Values Stray: A Short Summary Report

Assignment 3 of the term — compute a center, a spread, and an outlier fence from real data, read what each one says, and explain a summary choice to someone new to statistics.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. Last week you named a distribution's shape by its tail; this week two numbers, the mean and the median, back up that reading, and a spread and a fence say how far the values stray. This week's lecture tutorial, quiz, discussion, and Data Lab practise the same ideas from other angles; this assignment is where you put them together on one real decision.

The task

The Palmer penguins field log is a real observational dataset; 342 of its penguins have a recorded body mass, with mean 4,201.75 g and median 4,050 g, and a spreadsheet's QUARTILE.INC returns Q1 = 3,550 g and Q3 = 4,750 g for those masses, with the lightest bird at 2,700 g and the heaviest at 6,300 g. You will also use the six faces of a fair die, 1, 2, 3, 4, 5, and 6, whose mean and median are both 3.5.

Work these four problems, showing your arithmetic:

1. Someone types the six faces of a die into a spreadsheet as 1, 2, 3, 4, 5, 60, mistyping the 6 as 60. The six typed values add to 75. What is the mean of the typed values?
2. The 342 penguin body masses have a mean of 4,201.75 g and a median of 4,050 g. By how many grams does the mean exceed the median?
3. Treat the numbers 1, 2, 3, 4, 5, 6 as a sample of six rolls of a die. Their squared deviations from the mean of 3.5 add to 17.5. What is the sample variance?
4. For the 342 penguin body masses, Q1 = 3,550 g and Q3 = 4,750 g. What is the lower fence of the 1.5 × IQR rule, in grams?

Beside each answer, add one brief interpretation: what that value shows, and one use or limit of it. For problem 1, compare the mean with the median of the typed values. For problem 2, name the shape of the body-mass distribution by its tail. For problem 3, say what units the variance is in and which number you would report instead. For problem 4, say whether the lightest bird is flagged and what you would do with a value the rule flags.

Explain it to a non-expert

A volunteer who coordinates a community science program has never studied statistics and wants to tell new volunteers what a "typical" Palmer penguin weighs and how much the birds vary. Write a 3–5 sentence message that recommends one center and one measure of spread for penguin body mass, gives a reason tied to these data, and names one limit — for example, that a tail of heavy birds pulls the mean above the median, or that the field log is a sample of penguins, so the numbers describe these birds rather than every penguin. Explain any technical term in everyday words. More than one recommendation can be defensible.

For a different, ungraded example, imagine a neighborhood food bank manager who wants one number for a typical week's visitors and one for how much weeks vary, in a year when one holiday week was far busier than the rest. Model answer: "I'd report the median week, the week right in the middle when all the weeks are lined up, because one very busy holiday week would drag the average up. For how much weeks vary, I'd give the range of the middle half of the weeks, which that one busy week can't stretch. These numbers describe last year's visits, so they can't promise next year will look the same."

Use that pattern for the penguins, with your own recommendation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the volunteer coordinator before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about the center and spread of data. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data: the Palmer penguins field log, an observational dataset; 342 penguins have a recorded body mass, with mean 4,201.75 g and median 4,050 g, Q1 = 3,550 g and Q3 = 4,750 g from a spreadsheet's QUARTILE.INC, lightest 2,700 g and heaviest 6,300 g. The die: the six faces 1, 2, 3, 4, 5, 6, whose mean and median are both 3.5.
PROBLEM P1: Someone types the six faces of a die into a spreadsheet as 1, 2, 3, 4, 5, 60, mistyping the 6 as 60. The six typed values add to 75. What is the mean of the typed values?
PROBLEM P2: The 342 penguin body masses have a mean of 4,201.75 g and a median of 4,050 g. By how many grams does the mean exceed the median?
PROBLEM P3: Treat the numbers 1, 2, 3, 4, 5, 6 as a sample of six rolls of a die. Their squared deviations from the mean of 3.5 add to 17.5. What is the sample variance?
PROBLEM P4: For the 342 penguin body masses, Q1 = 3,550 g and Q3 = 4,750 g. What is the lower fence of the 1.5 × IQR rule, in grams?
After the four answers, I must briefly interpret each one: what that value shows and one use or limit of it; for P1, a comparison of the mean with the median of the typed values; for P2, the shape of the body-mass distribution named by its tail; for P3, the units of the variance and which number I would report instead; for P4, whether the lightest bird is flagged and what I would do with a flagged value. I must then write a 3-5 sentence message to a volunteer coordinator who is new to statistics, recommending one center and one measure of spread for penguin body mass with a reason tied to these data and naming one limit. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct center and spread computations (40 points), summary choice and shape reasoning (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct mean, difference, variance, or fence = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate account of what that value shows plus a use or limit tied to the die or penguin data = 2; exactly one of the two = 1; neither = 0. For P2, a skew named by where the pile sits instead of by its tail does not count. For P4, BOTH an accurate fence verdict for the lightest bird with the point that a flagged value is checked rather than deleted AND a final recommendation with a data-specific reason and a named limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0; naming a summary alone does not earn a unit. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to statistics, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my recommendation to the volunteer coordinator AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised summary report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised summary report with all four answers, their brief interpretations, and your message to the volunteer coordinator — written, or recorded as audio or video with a transcript, or as a labelled sketch of a boxplot with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

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.

Equivalent route (no AI required)

This route assesses the same Week 3 skills — computing a mean and seeing what one extreme value does to it, reading skew from the mean and the median, computing a sample variance with the right divisor, and applying the 1.5 × IQR rule — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to the volunteer coordinator. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised summary report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

Built with The Course Maker · samples.thecoursemaker.com