Subjects data analysis

Boxplot Comparison 59F9Be

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1. **State the problem:** We are comparing noon temperatures of two cities using box-and-whisker plots to answer questions about interquartile range (IQR), highest temperature, range, and median. 2. **Recall definitions:** - The **interquartile range (IQR)** is the difference between the third quartile (Q3) and the first quartile (Q1). - The **range** is the difference between the maximum and minimum values. - The **median** is the middle value of the data. 3. **Analyze City A:** - Whiskers from about 71 to 94, so range = $94 - 71 = 23$ - Median near 89 - Box (IQR) length is roughly from about 85 to 91 (estimated from plot), so IQR = $91 - 85 = 6$ 4. **Analyze City B:** - Whiskers from about 74 to 86, so range = $86 - 74 = 12$ - Median near 83 - Box (IQR) length roughly from about 78 to 84, so IQR = $84 - 78 = 6$ 5. **Answer questions:** (a) Which city had larger IQR? - Both have IQR about 6, so they are approximately equal. (b) Which city had highest noon temperature? - City A max is 94, City B max is 86, so City A has higher max. (c) Which city had smaller range? - City A range is 23, City B range is 12, so City B has smaller range. (d) Which city had larger median? - City A median is 89, City B median is 83, so City A has larger median. **Final answers:** (a) Both cities have approximately the same IQR. (b) City A had the highest noon temperature. (c) City B had the smaller range of noon temperatures. (d) City A had the larger median noon temperature.