Question

side-by-side box-and-whisker plots can be used to compare two or more different data sets. each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. the lengths (in seconds) of songs from two different concerts are shown. complete parts a through d below.

click here to view the box-and-whisker plots.

(a) describe the shape of each distribution. which concert has less variation in song lengths?

the distribution of concert 1 is

the distribution of concert 2 is

symmetric.
skewed right.
skewed left.

Explanation:

Analyze Concert 1 Symmetry

Using the Box Plot Symmetry and Distribution Shape Analysis knowledge points

• Five-number summary for Concert 1:
• Minimum: \(163\)
• \(Q_1\): \(256\)
• \(Q_2\) (Median): \(274\)
• \(Q_3\): \(310\)
• Maximum: \(333\)
• Left box width: \(Q_2 - Q_1 = 274 - 256 = 18\)
• Right box width: \(Q_3 - Q_2 = 310 - 274 = 36\)
• Left whisker length: \(Q_1 - \text{Min} = 256 - 163 = 93\)
• Right whisker length: \(\text{Max} - Q_3 = 333 - 310 = 23\)
• Since the left whisker is substantially longer than the right whisker, and the median is closer to the third quartile than the first quartile, the distribution is skewed left.

Analyze Concert 2 Symmetry

Using the Box Plot Symmetry and Distribution Shape Analysis knowledge points

• Five-number summary for Concert 2:
• Minimum: \(184\)
• \(Q_1\): \(202\)
• \(Q_2\) (Median): \(215\)
• \(Q_3\): \(228\)
• Maximum: \(247\)
• Left box width: \(Q_2 - Q_1 = 215 - 202 = 13\)
• Right box width: \(Q_3 - Q_2 = 228 - 215 = 13\)
• Left whisker length: \(Q_1 - \text{Min} = 202 - 184 = 18\)
• Right whisker length: \(\text{Max} - Q_3 = 247 - 228 = 19\)
• Since the left and right portions of the box and whiskers are highly symmetric, the distribution is symmetric.

Answer:

The distribution of Concert 1 is skewed left.

The distribution of Concert 2 is symmetric.