Question

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Explanation:

Analyze the definition of symmetry in box plots

Using the Symmetric Distribution knowledge point

A distribution is symmetric if its left half is a mirror image of its right half. For a box plot, this means:

• The median line is in the exact center of the box.
• The left whisker and right whisker are of equal length.

Evaluate the first option (a)

Using the Box Plot Symmetry knowledge point

Let's extract the key values from the box plot "Calories in Servings of Fruits":

• Minimum value: \(40\)
• First quartile (\(Q_1\)): \(50\)
• Median (\(Q_2\)): \(60\)
• Third quartile (\(Q_3\)): \(70\)
• Maximum value: \(80\)

Now, let's calculate the lengths of the sections:

• Left whisker length: \(Q_1 - \text{Min} = 50 - 40 = 10\)
• Right whisker length: \(\text{Max} - Q_3 = 80 - 70 = 10\)
• Left half of the box: \(Q_2 - Q_1 = 60 - 50 = 10\)
• Right half of the box: \(Q_3 - Q_2 = 70 - 60 = 10\)

Since all corresponding left and right sections are perfectly equal, this distribution is symmetric.

Answer:

• (a) Calories in Servings of Fruits (Correct answer)
• (b) Number of Text Messages Sent Today