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A farmer wonders if his crops grow better in sun or in shade. He measures the amount of fruit gathered from a sample of trees growing in full sun and from a sample of trees growing in mostly shade. The five number summaries, (minimum, Q1, median, Q3, maximum), follow:

Amount of fruit gathered from sunny trees: () bushels

Amount of fruit gathered from shady trees: () bushels

  1. On the same set of axes on grid paper, create a boxplot for each type of tree. Compare the center, shape, spread, and outliers of amount of fruit from sunny trees to the amount from shady trees.

    Example boxplots have been provided below.
    The blue one is for sunny trees, the red one is for shady trees.

    2 parallel Box Plots: Top: Left whisker: 10.8 to 13.3. Box: 13.3 to 58.1 with vertical line at 22.1. Right whisker: 58.1 to 100. Bottom: Left whisker: 10.9 to 18.5. Box: 18.5 to 61.5 with vertical line at 29.3. Right whisker: 61.5 to 127.

    Both data sets have similar spread, but the Q1, median, and Q3 are all higher in the shade. The maximum for the red boxplot is probably an outlier.

  2. The farmer wants to summarize the amount of fruit from each type of orchard with a mean and standard deviation. Is that appropriate? Explain.

    Standard deviation is best when the data is not skewed in one direction, and when there are not outliers. Is this data skewed? Are there outliers?