A comparison names shape, center, spread and outliers for both groups. Use comparative language: "A has a higher median than B", never two parallel descriptions. Name the variable and its units. Let the shape decide whether to quote means or medians.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Use comparative language
"Group A has median 12" and "Group B has median 9" is a list. "Group A has a higher median than Group B, 12 against 9 minutes" is a comparison. Write the word "than" into every sentence.
Always in context
"Higher median commute time, in minutes" beats "higher median". A comparison with no nouns from the problem earns nothing on the exam.
Choose measures consistently
For skewed data compare medians and IQRs. For symmetric data compare means and SDs. Do not mix a mean for one group with a median for the other.
Note the overlap
Two groups can differ in center while overlapping heavily. If A runs from 15 to 40 and B from 8 to 45, most of each group could have come from the other. Saying so is a stronger answer than the gap alone.
Outliers in a comparison
Name any outlier and which group it belongs to. "B has one commute of 95 minutes, far beyond its upper fence of 60." An outlier can be the most interesting point in the comparison.
The checklist
Shape of each. Which has the higher center, and by how much. Which has the greater spread. Any outliers. All in context with units. Four features, one paragraph, marks for each.
Step 2: Try It Yourself
Tap and try it out.
Test scores. Class 1: symmetric, mean 72, SD 8, range 55 to 90. Class 2: symmetric, mean 72, SD 15, range 40 to 98, one score at 20. Compare
- 1both roughly symmetric: means and SDsshape decides
Step 0 of 5
- 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: In Real Life
Two hospitals’ waits
One hospital has a lower median wait but a longer tail. Comparing shape, center and spread together tells a patient which is likely faster and which can be catastrophically slow.
Step 4: 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 5: 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?
The Choice
Problem 2 of 2
Both distributions are strongly skewed. Which center should be compared?
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 center?
4 of 8
Group A median 25, Group B median 18. Which is higher?
5 of 8
Is listing two separate descriptions a comparison?
6 of 8
Skewed right. Is the mean above or below the median?
7 of 8
Which belong in a full comparison?
8 of 8
Q1 = 20, Q3 = 26. What is the IQR?
Step 6: 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, center, spread and outliers.
- Use comparative language and name the variable in context.
- Let the shape decide whether to quote means or medians, and use the same measure for both groups.
- Note the overlap: groups can differ in center while overlapping heavily.