A comparison names shape, centre, spread and outliers for both groups. Missing one costs a mark on the exam.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Use comparative language
Say "Group A has a higher median than Group B", not "Group A has median 12". A list of two descriptions is not a comparison.
Always in context
Name the variable and its units. "Higher median commute time, in minutes" beats "higher median".
Choose measures consistently
For skewed data compare medians and IQRs. For symmetric data compare means and standard deviations.
Shape drives the choice
Decide the shape before choosing which centre to quote. That order prevents quoting a mean for badly skewed data.
Note the overlap
Two groups can differ in centre while overlapping heavily. Saying so is a stronger answer than reporting the gap alone.
Comparisons must be explicit
Saying "group A has median 12 and group B has median 9" is not a comparison. "Group A's median is higher than group B's" is. The exam requires comparative language, not two parallel descriptions.
Compare all four features
Shape, centre, spread and outliers, each compared directly between groups. A complete comparison addresses every one, and it does so in the context of the variable being measured.
Choose a display that permits comparison
Side-by-side boxplots, back-to-back stemplots, and overlaid dotplots all put groups on a common scale. A display with different scales for each group makes visual comparison meaningless.
Describing is not testing
Observing that one group's mean is higher describes the samples. Claiming the populations differ requires a significance test. Sliding from description to inference without a test is a specific and penalised error.
Step 2: Try It Yourself
Tap and try it out.
- Minimum4
- Lower quartile6
- Median9
- Upper quartile13
- Maximum18
- Interquartile range7
Each of the four sections holds a quarter of the values, however wide it looks. A narrow box means the middle half of the data is packed close together.
Step 3: Watch an Example
One step at a time.
Watch Amara Compare Two Groups
Group A commutes have median 25 minutes and IQR 10. Group B have median 18 and IQR 22, and both are right-skewed.
- Step 1
Both distributions are right-skewed, so medians and IQRs are the right measures.
Step 4: Your Turn
Practice makes it stick.
The Spread
Problem 1 of 2
Group A has IQR 10 and Group B has IQR 22. Which has greater spread? 1 A, 2 B.
The Choice
Problem 2 of 2
Both distributions are strongly skewed. Which centre should be compared? 1 mean, 2 median.
Compare Them
1 of 8
How many features should a comparison mention?
2 of 8
Q1 = 12, Q3 = 30. What is the IQR?
3 of 8
Symmetric data with no outliers. Which centre? 1 mean, 2 median.
4 of 8
Group A median 25, Group B median 18. Which is higher? 1 A, 2 B.
5 of 8
Is listing two separate descriptions a comparison? 1 yes, 0 no.
6 of 8
Skewed right. Is the mean above or below the median? 1 above, 2 below.
7 of 8
Which belong in a full comparison?
8 of 8
Q1 = 20, Q3 = 26. What is the IQR?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Q1 = 15, Q3 = 35. What is the IQR?
Question 2 of 2
What makes a comparison complete on the exam?
What You Learned
- Compare shape, centre, spread and outliers.
- Use comparative language and name the variable in context.
- Let the shape decide whether to quote means or medians.