Question

question 9 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 Box Plot Symmetry and Data Distribution Shape knowledge points

• Minimum value: \(13\)
• First quartile \(Q_1\): \(16\)
• Median \(Q_2\): \(17\)
• Third quartile \(Q_3\): \(22\)
• Maximum value: \(26\)

Analyze the skewness of the distribution

Using the Data Distribution Shape knowledge point

• Left side of the box: \(Q_2 - Q_1 = 17 - 16 = 1\)
• Right side of the box: \(Q_3 - Q_2 = 22 - 17 = 5\)
• Left whisker length: \(Q_1 - \text{Min} = 16 - 13 = 3\)
• Right whisker length: \(\text{Max} - Q_3 = 26 - 22 = 4\)
• The right side of the box is significantly wider than the left side, and the right whisker is longer than the left whisker, indicating a longer tail to the right. Thus, the distribution is skewed right.

Answer:

• Skewed left
• Skewed right (Correct answer)