Question

what is the shape of the distribution represented by the following box plot?

symmetric
skewed right

Explanation:

Identify key values from the box plot

Using the Box Plot Symmetry and Data Distribution Shape knowledge points

• Minimum value: \(11\)
• First quartile (\(Q_1\)): \(16\)
• Median (\(Q_2\)): \(19\)
• Third quartile (\(Q_3\)): \(22\)
• Maximum value: \(27\)

Analyze the symmetry of the components

Using the Box Plot Symmetry knowledge point

• Left whisker length: \(Q_1 - \text{Min} = 16 - 11 = 5\)
• Right whisker length: \(\text{Max} - Q_3 = 27 - 22 = 5\)
• Left box half width: \(Q_2 - Q_1 = 19 - 16 = 3\)
• Right box half width: \(Q_3 - Q_2 = 22 - 19 = 3\)

Determine the overall distribution shape

Using the Data Distribution Shape knowledge point

• Since both whiskers are equal in length (\(5\)) and both halves of the box are equal in width (\(3\)), the distribution is perfectly balanced on both sides of the median.
• Therefore, the shape of the distribution is symmetric.

Answer:

• Symmetric (Correct answer)
• Skewed right