Week 3 — Numerical Summaries: Center & Spread

Welcome to your Week 3 Start Here page.

Why this matters

One average can hide the story. A nurse comparing wait times and a small-business owner reading daily sales both need the middle and the spread.

In plain language

Last week you drew pictures of 12 month lengths and 342 penguin body masses; this week you put numbers on them. Two questions drive the whole chapter: where is the middle, and how spread out are the values? You will meet three ways to name the middle, called measures of center (single numbers that say where the middle of the data sits). You will also meet ways to measure spread (how far the values tend to stray from that middle). You will also learn which number to trust when one odd value shows up in your data.

• Already covered: Week 1, Foundations & Types of Data, taught you to tell a population from a sample and to sort every variable by its level of measurement. Week 2, Summarizing Data with Tables & Graphs, taught you to picture one variable and to describe its shape in words.
• This week: numbers for the middle (mean, median, mode), numbers for the spread (range, variance, standard deviation, IQR), the boxplot, and a rule for flagging unusual values.
• How they connect: the level of measurement from Week 1 decides which center you may use, and the shape from Week 2 decides which center tells the truth.
• Where we're going next: Week 4, Exploring Relationships Between Two Variables, moves from one variable to two and asks whether they move together.

Focus

What is typical, and how far do values stray from it?

By the end of this module, you should be able to:

• [ ] find the mean, median, and mode, and pick the one a variable allows
• [ ] explain why one wild value moves the mean but not the median
• [ ] compute a standard deviation with the right divisor
• [ ] build a five-number summary and apply the 1.5 × IQR rule

To-do

Plan your week

1. Read Chapter 3 (about 40 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

Checkpoint: find the median and IQR of the twelve month lengths, and say whether February is flagged.

You've got this

Take it in order, and ask your instructor early if a step snags.

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