4) The heights (in inches) of ten different trees in a park were recorded as: \( 50,55,60,45,52,48,62,58,54,59 \) a) Identify the 5-number summary for this data. Minimum: Q1: Median: b) What is the interquartile range? c) Construct a box plot for the data.

To find the 5-number summary for the tree heights: 1. **Minimum**: This is the smallest value in the dataset, which is \( 45 \) inches. 2. **Q1 (First Quartile)**: This cuts off the lowest 25% of the data. The sorted heights are \( 45, 48, 50, 52, 54, 55, 58, 59, 60, 62 \). Q1, being the median of the first half, is \( 50 \). 3. **Median**: The median is the middle value of the sorted data, which is the average of the 5th and 6th values: \( (54 + 55)/2 = 54.5 \). 4. **Q3 (Third Quartile)**: This is the median of the upper half of the dataset, which is \( 58 \). 5. **Maximum**: This is the largest value in the dataset, which is \( 62 \). So, summarizing: **Minimum: 45, Q1: 50, Median: 54.5, Q3: 58, Maximum: 62.** b) The interquartile range (IQR) is calculated as \( Q3 - Q1 \), which gives \( 58 - 50 = 8 \) inches. c) To construct a box plot: - Draw a number line and mark the 5-number summary \( 45, 50, 54.5, 58, 62 \). - The box extends from Q1 to Q3 (from \( 50 \) to \( 58 \)) with a line at the median (\( 54.5 \)). - Draw lines (whiskers) from the box to the minimum and maximum values, completing the box plot. Now you've got a complete understanding of your tree heights! Happy analyzing! 🌳📊