Bridging the Gap

Learning Focus

Compare two distributions using center and spread, and write conclusions in context.

Big idea

To compare data sets, discuss shape, center, and spread.

• Compare means with SD, or medians with IQR.
• The same center can come with very different spread.
• Express differences in context, e.g. in multiples of the spread.

Worked example

Class A mean is $78$; Class B mean is $71$. Difference: $78-71=7$ points.

Team A median $14$, Team B median $20$, both IQR $4$. Difference in medians is $6$, which is $\frac{6}{4}=1.5$ IQRs.

Data $10,10,10,10,10$ and $0,5,10,15,20$ both have mean $10$, but the second is far more spread out.

Takeaways

• Match center with spread.
• Subtract centers to compare.
• Say which group is higher and by how much.