CASE STUDY

The Beatles' Song Length

In the article "Length of The Beatles' Songs" (Chance, Vol. 25, No. 1, pp. 30-33), T. Koyama

discusses aspects and interpretations of the lengths of songs by The Beatles. In this case study, we concentrate on the 175 songs that appear in The Beatles' 12 studio record albums.

The following table provides some basic information about the studio albums. At the end of this chapter, you will find the data on album name and length, in seconds, of each song in an album.

As noted by Professor Koyama, the B-side of Yellow Submarine consists of six instrumental songs composed by George Martin and another song credited to Lennon and McCartney and arranged by George Martin, none of which are considered Beatles' songs.

Note that the albums are ordered by release date (Please Please Me was the first album released, With the Beatles was the second, etc.). The song-length data for each album is arranged in increasing order.

Choose three albums to work with. I would suggest choosing one of the earlier albums, one album around the middle, and one of the later albums.

1. Determine the median song length of each album.
2. Construct a graph with album name on the horizontal axis and median song length on the vertical axis. Interpret your graph, keeping in mind that albums are ordered by release date.
3. Determine the range of song lengths for each album.
4. Construct a graph with album name on the horizontal axis and range of song lengths on the vertical axis. Interpret your graph.
5. Find the quartiles of song length for each album.
6. Determine the IQR of song lengths for each album.
7. Construct a graph with album name on the horizontal axis and IQR of song lengths on the vertical axis. Interpret your graph.
8. Find the lower and upper limits of song length for each album. Use them to identify potential outliers.
9. For each album, construct a boxplot of the song lengths, and interpret your results in terms of the variation of the song lengths.
10. This week, we learned about measures of center and spread. Are there any applications from this week’s content to your major, your profession, or your interests? Please explain.

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