Question

The median of Jonah’s data set is greater. So the students at Jonah’s school generally spend more hours on homework each week than the students at Finn’s school.


The interquartile range of Finn’s data set is greater. So there is greater variability, or spread, in the number of hours students in Finn’s school spend on homework.

Answer 1

Both statements are reasonable interpretations of the two summary measures, with a couple of important caveats.

- Median: If Jonah’s median is larger than Finn’s, that means the middle student at Jonah’s school has a higher homework-hours value than the middle student at Finn’s school. It is correct to say Jonah’s students “generally” spend more time — median compares central tendency — but this does not mean every Jonah student spends more time, nor does it say anything about the size of the difference or whether it is statistically meaningful.

- Interquartile range (IQR): If Finn’s IQR is larger, the middle 50% of Finn’s students have a wider spread of homework hours than the middle 50% at Jonah’s. That indicates greater variability among the typical (central) students at Finn’s. The IQR does not reflect extreme values (outliers) or the full range, so Finn could still have a smaller overall range or different outliers.

If you need a stronger or more complete comparison, also look at sample sizes, means and standard deviations, full range and outliers, or perform a statistical test.