Comparative Statistics Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Box plots for two classes show: Class A median=70, IQR=20. Class B median=75, IQR=5. Which class has better performance? Which is more consistent?

Solution

  1. 1
    Better performance (center): Class B has higher median (75 > 70)
  2. 2
    More consistent (spread): Class B has smaller IQR (5 < 20) — less spread in the middle 50%
  3. 3
    Class A: lower median, more variable scores (some very high, some very low)
  4. 4
    Class B: higher median AND more consistent — clearly superior on both dimensions

Answer

Class B: higher median (75) and more consistent (IQR=5). Superior on both center and spread.
When comparing distributions, evaluate both center (who scores higher on average) and spread (who is more consistent). Class B dominates on both, making it clearly preferable. In practice, trade-offs often occur — one group has higher mean but lower consistency.

About Comparative Statistics

Comparative statistics involves using statistical measures to compare two or more groups, data sets, or distributions.

Learn more about Comparative Statistics →

More Comparative Statistics Examples

Example 1 easy

Compare two groups on a test: Group A ([formula]): mean=75, SD=10. Group B ([formula]): mean=82, SD=

Example 2 medium

Three products have customer satisfaction scores. Product A: mean=4.2, SD=0.5 (n=50). Product B: mea

Example 4 hard

Men: mean height = 70", SD = 3". Women: mean height = 64", SD = 2.5". A person is 67" tall. Calculat

← All Comparative Statistics Examples Comparative Statistics Concept