Cogito
AP Statistics · Chapter 1 · Lesson 1
Describing a Distribution
Shape, centre, spread, and the odd one out.
11 problems · about 24 minutes · AP Statistics 1.5, 1.6, 1.7
What this lesson teaches
The student describes a distribution by shape, centre, spread, and outliers, and chooses a suitable summary.
- Describe a distribution by shape, centre, spread, and outliers.
- Skew drags the mean towards the tail; the median stays put.
- Report median and IQR when skewed, mean and standard deviation when symmetric.
Warm Up
Straightforward practice. Get the method working first.
4 problemsValues 3, 7, 8, 9, 200. What is the median?
Answer 8
Why 8.
Values 2, 4, 6. What is the mean?
Answer 4
Why 12 ÷ 3.
Values 1, 2, 3, 4, 90. What is the median?
Answer 3
Why The middle one.
Q1 = 10 and Q3 = 22. What is the IQR?
Answer 12
Why Q3 − Q1.
Build It Up
The same ideas with more to keep track of.
3 problemsSort each measure by whether an outlier moves it much.
Answer Resistant: Median, IQR · Sensitive: Mean, Standard deviation
Why Anything built from every value is sensitive.
Left-skewed. Is the mean below the median? 1 for yes, 0 for no.
Answer 1
Why The tail is on the left.
Roughly symmetric with no outliers. Report the mean? 1 for yes, 0 for no.
Answer 1
Why Nothing is dragging it.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsValues 5, 5, 5, 5. What is the standard deviation?
Answer 0
Why No spread at all.
Order the four things you describe about any distribution.
Answer 1. Shape 2. Centre 3. Spread 4. Outliers
Why Shape first, because it decides which centre to report.
The Median: Values 4, 8, 9, 12, 100. What is the median?
Answer 9
Why 9.
The Skew: In a right-skewed distribution, is the mean above the median? 1 for yes, 0 for no.
Answer 1
Why Yes.