Question

use the box-and-whisker plot to determine if the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these.

choose the correct answer below.

skewed right
symmetric
skewed left
none of these

Explanation:

Identify the key values from the box-and-whisker plot

We first read the five-number summary values directly from the horizontal axis of the box-and-whisker plot:

• Minimum value (leftmost point): \(0\)
• First quartile \(Q_1\) (left edge of the box): \(60\)
• Median \(Q_2\) (vertical line inside the box): \(110\)
• Third quartile \(Q_3\) (right edge of the box): \(160\)
• Maximum value (rightmost point): \(220\)

Analyze the symmetry of the box

We compare the distances from the median to the first and third quartiles:

• Distance from \(Q_1\) to Median: \(110 - 60 = 50\)
• Distance from Median to \(Q_3\): \(160 - 110 = 50\)

Since these distances are equal, the middle \(50\%\) of the data is perfectly symmetric about the median.

Analyze the symmetry of the whiskers

We compare the lengths of the left and right whiskers:

• Left whisker length (from Minimum to \(Q_1\)): \(60 - 0 = 60\)
• Right whisker length (from \(Q_3\) to Maximum): \(220 - 160 = 60\)

Since the whisker lengths are also equal, the outer parts of the distribution are symmetric.

Determine the overall shape of the distribution

Because both the box and the whiskers are perfectly balanced and symmetric about the median, the overall shape of the distribution represented by this box-and-whisker plot is symmetric.

Answer:

• skewed right
• symmetric (Correct answer)
• skewed left
• none of these