1. The problem is to find the interquartile range (IQR) of the given data set: 585, 1500, 1562, 1645, 1710, 1719, 1762, 1798, 1814, 2001, 2018, 2026, 2057, 2173, 2213, 2258, 2365, 2516, 2545, 2890. 2. The interquartile range (IQR) is calculated as $$\text{IQR} = Q_3 - Q_1$$ where $Q_1$ is the first quartile (25th percentile) and $Q_3$ is the third quartile (75th percentile). 3. First, order the data (already ordered): 585, 1500, 1562, 1645, 1710, 1719, 1762, 1798, 1814, 2001, 2018, 2026, 2057, 2173, 2213, 2258, 2365, 2516, 2545, 2890. 4. The number of data points $n=20$. 5. To find $Q_1$, find the median of the lower half (first 10 values): 585, 1500, 1562, 1645, 1710, 1719, 1762, 1798, 1814, 2001. 6. The median of these 10 values is the average of the 5th and 6th values: $$Q_1 = \frac{1710 + 1719}{2} = \frac{3429}{2} = 1714.5$$ 7. To find $Q_3$, find the median of the upper half (last 10 values): 2018, 2026, 2057, 2173, 2213, 2258, 2365, 2516, 2545, 2890. 8. The median of these 10 values is the average of the 5th and 6th values: $$Q_3 = \frac{2213 + 2258}{2} = \frac{4471}{2} = 2235.5$$ 9. Calculate the interquartile range: $$\text{IQR} = Q_3 - Q_1 = 2235.5 - 1714.5 = 521$$ 10. Therefore, the interquartile range of the data set is 521.