Question: Here is a sample data set. 575 584 369.5 608.2 615.3 478.7 534.6 494.2 464.4 504.3 509.7 474.5 464.4 453.9 466.7 503.9 345.8 529 401.6 391.8 544.9 572.2 576.4 566.2 500.4 499.3 421.9 572.2 591.1 433.3 357.8 566.5 512.2 509.7 422.1 572.2 566.7 363.6 395.1 359.2 596.6 581.8 528.8 583.4 464.4 566.7 500.6 553.7 596.9 521.9 481.1 473.9 573.4 608.7 Use a calculator/technology to answer the following. Find the first quartile for this data set. Q₁ = Find the third quartile for this data set. Q₃ = Find the interquartile range for this data set. IQR = Q₃ − Q₁ =

1. **State the problem:** We are given a data set of 54 values and need to find the first quartile ($Q_1$), third quartile ($Q_3$), and the interquartile range (IQR). 2. **Organize the data:** Sort all 54 values in ascending order. 3. **Find $Q_1$:** The first quartile is the median of the lower half of the data (below the overall median). Since $n=54$, the lower half has 27 values. $Q_1$ is the 14th value in the sorted list. 4. **Find $Q_3$:** The third quartile is the median of the upper half of the data (above the overall median). The upper half also has 27 values. $Q_3$ is the 14th value in the upper half, or the 41st value overall. 5. **Calculate IQR:** $\text{IQR} = Q_3 - Q_1$ --- **Sorted data (ascending):** 345.8, 357.8, 359.2, 363.6, 369.5, 391.8, 395.1, 401.6, 422.1, 421.9, 433.3, 453.9, 464.4, 464.4, 464.4, 466.7, 466.7, 473.9, 474.5, 478.7, 481.1, 494.2, 499.3, 500.4, 500.6, 503.9, 504.3, 509.7, 509.7, 512.2, 521.9, 528.8, 529, 534.6, 553.7, 566.2, 566.5, 566.7, 566.7, 572.2, 572.2, 572.2, 573.4, 575, 576.4, 581.8, 583.4, 584, 591.1, 596.6, 596.9, 608.2, 608.7, 615.3 - $Q_1$ is the 14th value: $464.4$ - $Q_3$ is the 41st value: $572.2$ 6. **Calculate IQR:** $$\text{IQR} = Q_3 - Q_1 = 572.2 - 464.4 = 107.8$$ **Final answers:** - $Q_1 = 464.4$ - $Q_3 = 572.2$ - $\text{IQR} = 107.8$