Question

ex2) make a dot plot for the given data. then describe the shape of its distribution. {5, 6, 4, 4, 6, 7, 4, 5, 4}

Explanation:

Step1: Count data occurrences

Count how many times each number appears:

• \( 4 \): occurs \( 4 \) times (\( 4, 4, 4, 4 \))
• \( 5 \): occurs \( 2 \) times (\( 5, 5 \))
• \( 6 \): occurs \( 2 \) times (\( 6, 6 \))
• \( 7 \): occurs \( 1 \) time (\( 7 \))
• \( 1,2,3,8,9 \): \( 0 \) times

Step2: Create dot plot

On the number line (with ticks for \( 1,2,3,4,5,6,7,8,9 \)):

• Above \( 4 \): draw \( 4 \) dots.
• Above \( 5 \): draw \( 2 \) dots.
• Above \( 6 \): draw \( 2 \) dots.
• Above \( 7 \): draw \( 1 \) dot.
• Above \( 1,2,3,8,9 \): no dots.

Step3: Describe distribution shape

The data has the most dots at \( 4 \) (left - side peak), and as values increase (toward \( 7 \)), frequency decreases. So the distribution is right - skewed (or positively skewed), with a peak at \( 4 \) and a tail extending to the right (toward larger values like \( 7 \)).

Answer:

Dot Plot:

• Ticks: \( 1, 2, 3, 4, 5, 6, 7, 8, 9 \)
• Dots:
• \( 1,2,3,8,9 \): \( 0 \) dots
• \( 4 \): \( \boldsymbol{\cdot\cdot\cdot\cdot} \)
• \( 5 \): \( \boldsymbol{\cdot\cdot} \)
• \( 6 \): \( \boldsymbol{\cdot\cdot} \)
• \( 7 \): \( \boldsymbol{\cdot} \)

Distribution Shape:

The distribution is right - skewed (positively skewed). It has a peak at \( 4 \), and the data values tend to tail off toward the right (larger values).