Week 3 — A Typical Value and How Far Values Stray: A Short Summary Report — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned to name the middle of a dataset three ways, to see which middle resists one wild value, to read skew from the mean and the median, to measure spread with the right divisor, and to flag unusual values with the 1.5 × IQR rule. Last week you named a distribution's shape by its tail; this week two numbers back up that reading. In this assignment you work four short problems on real data, interpret each one, and explain a summary choice to someone who has never studied statistics. This week's lecture tutorial, quiz, discussion, and Data Lab practise the same ideas from other angles.

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.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

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.

Deliverables

Submit a single summary report containing:

• the four answers, each with the arithmetic shown and a brief interpretation of what that value shows and one use or limit of it;
• your message to the volunteer coordinator, recommending one center and one measure of spread for penguin body mass with a reason tied to these data and naming one limit; and
• a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of a boxplot with a short note. Every form is graded by the same scoring criteria. 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.

How you'll be graded

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

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's numbers, is an integrity violation under the course policy.

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