Question

ox plots - item 20909
he two plots compare the top 25 home run hitters in 2007 with those in 2008.
which choice is not true?
the median number of home runs in 2007 is equal to
the minimum value for 2008.
the interquartile range for both 2007 and 2008 is the
same.
the highest number of home runs hit in 2007 is more
than in 2008.
the range of values for 2007 is greater than the rang
for 2008.

Explanation:

Step1: Analyze the range

• For 2007: The range is calculated as \( \text{Range}_{2007}=\text{Max}_{2007}-\text{Min}_{2007}\). From the box - plot, assume \( \text{Max}_{2007}\) is a value (say \(x\)) and \( \text{Min}_{2007}\) is a value (say \(y\)).
• For 2008: The range is \( \text{Range}_{2008}=\text{Max}_{2008}-\text{Min}_{2008}\). From the box - plot, \( \text{Max}_{2008}\) is larger than \( \text{Max}_{2007}\) and \( \text{Min}_{2008}\) is larger than \( \text{Min}_{2007}\). Calculate \( \text{Range}_{2007}\) and \( \text{Range}_{2008}\).

Step2: Check each option

• Option 1: Check if the median of 2007 equals the minimum of 2008 from the box - plots.
• Option 2: Calculate the inter - quartile range (\(IQR = Q_3 - Q_1\)) for 2007 and 2008. If \(IQR_{2007}=IQR_{2008}\), this option is true.
• Option 3: Compare the maximum values of 2007 and 2008 from the box - plots.
• Option 4: Calculate the range (\(Range=\text{Max}-\text{Min}\)) for 2007 and 2008. From the box - plots, \( \text{Range}_{2008}\) is larger than \( \text{Range}_{2007}\).

Answer:

The range of values for 2007 is greater than the range for 2008 (This option is NOT true)