Question 1: A scientist recorded the heights (in cm) of 12 different types of trees in a rainforest. The heights are: 150, 165, 160, 155, 170, 180, 145, 155, 165, 160, 175, 150. Calculate the five-number summary for these tree heights.

Answer: Minimum: 145, Q1: 150, Median: 160, Q3: 165, Maximum: 180

Question 2: Using the data from Question 1, sketch a box plot that represents the distribution of tree heights.

Answer: Student draws the box plot on the grid.

Question 3: A survey recorded the daily rainfall (mm) over a month in a rainforest. The recorded values are: 5, 12, 8, 15, 20, 18, 22, 25, 10, 12, 14, 19, 17, 23, 30, 25, 28, 26, 21, 19, 16, 14, 11, 9, 13, 15, 20, 22, 24, 27. Find the five-number summary for the rainfall data.

Answer: Minimum: 5, Q1: 11, Median: 18, Q3: 24, Maximum: 30

Question 4: Construct a box plot to represent the rainfall data from Question 3. Ensure your plot is accurate and clearly labeled.

Answer: Student draws box plot on the grid.

Question 5: A researcher measures the length (cm) of different fish caught in a river over a week. The data are: 30, 45, 50, 55, 60, 65, 70, 75, 80, 85. Calculate the median length of the fish.

Answer: Median: 60

Question 6: The length data from Question 5 is skewed. Explain whether the median is a good measure for the typical fish length and why.

Answer: The median is good if the data is skewed because it is less affected by extreme values than the mean.

Question 7: A study recorded the number of leaves on different trees in a forest. The data: 200, 220, 210, 230, 240, 250, 260, 270, 280, 300. Find the interquartile range (IQR) of this data.

Answer: Q1: 210, Q3: 270, IQR: 60

Question 8: The forest survey shows a maximum leaf count of 300 and a minimum of 200. If the interquartile range is 60, what are the approximate Q1 and Q3 values?

Answer: Q1 ≈ 210, Q3 ≈ 270

Question 9: A new set of environmental data shows the number of birds observed per day: 12, 15, 14, 13, 16, 19, 21, 23, 22, 20. Determine the five-number summary.

Answer: Minimum: 12, Q1: 13, Median: 17, Q3: 21, Maximum: 23

Question 10: Compare the five-number summaries of bird counts and rainfall data. What do the differences tell you about the variability in these environmental factors?

Answer: The bird count has a smaller range and more consistent data, indicating less variability, while rainfall varies more widely.

Question 11: Identify a common mistake students make when calculating the five-number summary and suggest how to avoid it.

Answer: A common mistake is including outliers as part of the minimum or maximum; students should check for true extremes and consider outliers separately.