Question

question 37 points 3

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

skewed left

skewed right

Explanation:

Identify key values from the box plot

Using the Data Distribution Shape knowledge point

• Minimum value: \(10\)
• First quartile (\(Q_1\)): \(16\)
• Median (\(Q_2\)): \(20\)
• Third quartile (\(Q_3\)): \(22\)
• Maximum value: \(23\)

Analyze the lengths of the whiskers

Using the Box Plot Symmetry knowledge point

• Left whisker length: \(Q_1 - \text{Minimum} = 16 - 10 = 6\)
• Right whisker length: \(\text{Maximum} - Q_3 = 23 - 22 = 1\)
• The left whisker is significantly longer than the right whisker.

Analyze the box asymmetry

Using the Box Plot Symmetry knowledge point

• Left half of the box: \(Q_2 - Q_1 = 20 - 16 = 4\)
• Right half of the box: \(Q_3 - Q_2 = 22 - 20 = 2\)
• The left side of the box is wider than the right side.

Determine the skewness direction

Using the Skewness Direction and Left Skewness knowledge points

• Since both the left whisker and the left side of the box are longer, the data is stretched out further to the left.
• This indicates a distribution with a long tail on the left side, which is classified as skewed left.

Answer:

• Skewed left (Correct answer)
• Skewed right