Question

comparing data sets with boxplots
oyster volume(cc)
mussel volume(cc)
which statements are true regarding the data
displayed in the boxplots? check all that apply
the median for the mussel volume is greater than
the median for the oyster volume.
the range in data for the oyster volume is greater
than for the mussel volume.
oysters tend to have more volume than mussels.
the iqr is less for the mussel volume than for the
oyster volume.
there is greater variation of oyster volumes than
mussel volumes.

Explanation:

• Median: The line inside the box of a box - plot represents the median. For mussel volume, the median is around 10, and for oyster volume, the median is around 11. So, the median for the oyster volume is greater than the median for the mussel volume.
• Range: The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). For mussel volume, \( \text{Range}=13 - 7.5=5.5 \). For oyster volume, \( \text{Range}=15 - 6 = 9 \). So, the range in data for the oyster volume is greater than for the mussel volume.
• Inter - Quartile Range (IQR): The IQR is calculated as \( \text{IQR}=Q_{3}-Q_{1} \). For mussel volume, \( Q_{1} = 8.5, Q_{3}=10.5,\text{IQR}=10.5 - 8.5 = 2 \). For oyster volume, \( Q_{1}=8, Q_{3}=13,\text{IQR}=13 - 8=5 \). So, the IQR is not less for the mussel volume than for the oyster volume.
• General Tendency: Since the oyster volume box - plot (on average, as measured by the median) is shifted to the right compared to the mussel volume box - plot, oysters tend to have more volume than mussels.
• Variation: Variation can be measured by the range or IQR. Since the range (and IQR) of oyster volume is larger than that of mussel volume, there is greater variation of oyster volumes than mussel volumes.

Answer:

• The median for the oyster volume is greater than the median for the mussel volume.
• The range in data for the oyster volume is greater than for the mussel volume.
• Oysters tend to have more volume than mussels.
• There is greater variation of oyster volumes than mussel volumes.