25.5 Comparing distributions and outliers — Practise

1. H Group A has $Q_1=8$ and $Q_3=17$. Group B has $Q_1=10$ and $Q_3=23$. Find each IQR and identify the greater middle-half spread.
2. H The median waiting time is 12 minutes at Clinic A and 17 minutes at Clinic B. Which clinic has the lower typical wait, using the median?
3. H A data set has $Q_1=20$ and $Q_3=32$. Find the lower and upper fences using $1.5\times\mathrm{IQR}$.
4. H The upper fence is 40. A value is 46. Does the IQR rule flag it as a possible outlier?
5. H A distribution has minimum 4, maximum 50, $Q_1=12$ and $Q_3=20$. Find its range and IQR.
6. H For the travel times, $Q_1=17.5$, $Q_3=26.5$, and the maximum is 42. Use the upper IQR fence to check whether 42 is a possible outlier.
7. H Two groups have the same median. Group A has IQR 5 and Group B has IQR 11. Which group has more variation in the middle half?
8. H A distribution has $Q_1=14$ and IQR 6. Find the lower fence.
9. H Group X has median 30 and IQR 8. Group Y has median 25 and IQR 8. Compare their typical values and middle-half spreads.
10. H To compare the spread of two distributions that include an extreme value, which measure is safer: the range or the IQR? Give a reason. Then, for $Q_1=12$, $Q_3=28$ and a maximum of 50, find the IQR and decide whether 50 is an outlier.