Describe every distribution the same way: shape, centre, spread, and any outliers.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Skew pulls the mean
In a right-skewed distribution the mean sits above the median, dragged by the long tail.
Resistant measures
The median and the interquartile range barely move when an outlier is added. The mean and standard deviation do.
What to report
Skewed or with outliers, report median and IQR. Roughly symmetric, report mean and standard deviation.
Shape, centre, spread, outliers
A complete description of a distribution names all four, in context. Omitting any one loses credit on the exam, and omitting context — naming the variable and the units — loses it too.
Naming the shape
Symmetric, skewed left, skewed right, uniform, or bimodal. Skewness is named for the direction of the long tail, not the bulk of the data, which is the opposite of most people's first instinct.
Which measures suit which shape
For roughly symmetric data use mean and standard deviation; for skewed data or data with outliers use median and interquartile range. The median and IQR are resistant, which is what makes them appropriate there.
Outliers are investigated, not deleted
The 1.5 × IQR rule flags candidates. A flagged point may be a data entry error or a genuine extreme value, and the two call for different responses. Deleting one because it is inconvenient is misconduct, not method.
Step 2: Try It Yourself
Change the counts and watch the shape change.
Low
Mid-low
Mid-high
High
There are 16 in all.
Low has the most. It has 7 more than High.
Step 3: Watch an Example
One step at a time.
Watch Rosa Choose a Summary
Rosa has incomes: 21, 24, 26, 28, and 400 (in thousands).
- Step 1
The 400 is far from the rest, so it is an outlier.
Step 4: Your Turn
Practice makes it stick.
The Median
Problem 1 of 2
Values 4, 8, 9, 12, 100. What is the median?
The Skew
Problem 2 of 2
In a right-skewed distribution, is the mean above the median? 1 for yes, 0 for no.
Summarise It
1 of 8
Values 2, 4, 6. What is the mean?
2 of 8
Values 1, 2, 3, 4, 90. What is the median?
3 of 8
Q1 = 10 and Q3 = 22. What is the IQR?
4 of 8
Sort each measure by whether an outlier moves it much.
Tap something to move it.
- Empty
- Empty
5 of 8
Left-skewed. Is the mean below the median? 1 for yes, 0 for no.
6 of 8
Roughly symmetric with no outliers. Report the mean? 1 for yes, 0 for no.
7 of 8
Values 5, 5, 5, 5. What is the standard deviation?
8 of 8
Order the four things you describe about any distribution.
- 1Centre
- 2Spread
- 3Outliers
- 4Shape
Step 5: Quick Check
Show what you know.
Question 1 of 1
Values 3, 7, 8, 9, 200. What is the median?
What You Learned
- 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.