Question

3 the boxplot below shows barley production compared across six farms in the 1930s. yields by farm deluth canal rapids crookston morris waseca university farm 0 5 10 15 20 25 30 35 40 45 50 55 60 63 70 which farm has a median value yield closest to 40? crookston which farm has the largest variability as measured by interquartile range (iqr)?

Explanation:

To determine which farm has the largest variability as measured by the Interquartile Range (IQR), we analyze the boxplots:

• The IQR of a boxplot is the length of the box (from the first quartile \( Q_1 \) to the third quartile \( Q_3 \), so \( \text{IQR} = Q_3 - Q_1 \)). A longer box indicates a larger IQR (more variability in the middle 50% of the data).
• Visually inspecting the boxplots:
• Delath: Short box.
• Grand Rapids: Moderate box.
• Crookston: Moderate box.
• Morris: Moderate box.
• Waseca: The longest box (spanning the most horizontal distance).
• University Farm: Short box.

Thus, the farm with the largest IQR (most variability) is Waseca.

Answer:

Waseca