25.1 Quartiles, interquartile range and box plots — Practise

1. H Find the median, lower quartile and upper quartile of $3, 5, 7, 8, 10, 12, 14, 18$.
2. H The quartiles are $Q_1=14$ and $Q_3=26$. Work out the interquartile range.
3. H For $4, 6, 8, 9, 11, 13, 15, 20$, write the five-number summary using the median-of-halves convention.
4. H A box plot has minimum $5$, lower quartile $9$, median $12$, upper quartile $18$ and maximum $23$. Work out its IQR and range.
5. H Group A has $Q_1=11$ and $Q_3=19$. Group B has $Q_1=8$ and $Q_3=21$. Which group has the larger middle-half spread?
6. H For $2, 4, 5, 7, 9, 10, 12, 16, 18, 20$, find the median and quartiles using the median-of-halves convention.
7. H The lower quartile is $32$ and the IQR is $15$. Work out the upper quartile.
8. H The middle half of one group lies between $24$ and $38$. Work out the IQR and state what it measures.
9. H A box plot uses a scale from $0$ to $50$. Its median is at $30$, and its quartiles are $18$ and $36$. Work out the IQR.