Question

Song Lengths 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 played at two different concerts are shown.

Side-by-side box-and-whisker plots comparing song lengths from Punk Rock and Jazz concerts, measured in seconds.

d. Can you determine which concert lasted longer? Explain.

Accepted Answer

Step 1: Observe the box-and-whisker plots for both concerts. The Punk Rock Concert has song lengths ranging from 177 seconds (minimum) to 240 seconds (maximum), while the Jazz Concert has song lengths ranging from 200 seconds (minimum) to 390 seconds (maximum). Step 2: Compare the interquartile ranges (IQRs) of the two concerts. The Punk Rock Concert has an IQR from 200 seconds (Q1) to 220 seconds (Q3), while the Jazz Concert has an IQR from 224 seconds (Q1) to 288 seconds (Q3). This indicates that Jazz songs tend to be longer on average. Step 3: Analyze the medians of the two data sets. The median for the Punk Rock Concert is 210 seconds, while the median for the Jazz Concert is 275 seconds. This further supports that Jazz songs are generally longer. Step 4: Consider the maximum song lengths. The longest song in the Punk Rock Concert is 240 seconds, whereas the longest song in the Jazz Concert is 390 seconds. This suggests that the Jazz Concert likely lasted longer due to longer individual songs. Step 5: Conclude that the Jazz Concert likely lasted longer because its songs have higher medians, a wider range, and longer maximum song lengths compared to the Punk Rock Concert.

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Key Concepts

Box-and-Whisker Plot

Quartiles

Comparison of Data Sets