Question

question 31 points 2

which of the following is true about the distribution shown below?

parasailing costs ($)

bi-modal

skewed left

Explanation:

Analyze the dot plot

Using the Dot Plot Interpretation knowledge point
The dot plot shows the frequency of parasailing costs from \$30 to \$40. Let's list the frequencies (number of 'x' marks) for each value:

• 31: 1
• 32: 3
• 33: 2
• 34: 4
• 35: 4
• 36: 2
• 37: 3
• 38: 2
• 39: 1

Evaluate distribution shape

Using the Symmetric Distribution knowledge point
Let's check the symmetry of the distribution around its center. The center of the data range is at 35.

• Frequencies at equal distances from 35:
• 34 and 35 both have 4.
• 33 and 36 both have 2.
• 32 and 37 both have 3.
• 31 and 38 have 1 and 2 respectively (very close to symmetric).
• 30 and 39 have 0 and 1 respectively.

The overall shape is balanced on both sides, indicating a symmetric distribution rather than a skewed one.

Evaluate modality

Using the Bimodal Distribution knowledge point
A bimodal distribution has two distinct peaks (local maxima) separated by a valley.

• Here, the highest frequency is 4, which occurs at both 34 and 35.
• These two peaks are adjacent to each other, forming a single central peak area rather than two separated peaks.
• Therefore, the distribution is unimodal (symmetric and bell-shaped), not bi-modal.

Determine the correct option

Since the distribution is symmetric and bell-shaped, it is best described as symmetric.

• "Bi-modal" is incorrect because there are no two separated peaks.
• "Skewed left" is incorrect because the tail is not stretched to the left.
• "Symmetric" is the correct description of this balanced, bell-like shape.

Answer:

• Bi-modal
• Skewed left
• Symmetric (Correct answer)