Part 1: Understanding the Big Ideas
Recall that for Lab Activity #5, we worked with some Rock and Roll Hall of Fame data. In 1988, The Beatles were inducted into the Rock and Roll Hall of Fame. The Beatles released 12 studio albums in the United Kingdom. For this part of our lab activity, we will focus on looking at the lengths, in seconds, of the 175 songs included on these albums. The two graphical displays below, and the accompanying table of summary statistics, should be used to answer Questions 1 through 9.
Mean Standard Deviation Minimum Q1 Median Q3 Maximum
- The individuals in this sample of data areA. Beatles B. albums. C. lyrics. D. songs. E. seconds.
- How would you describe the shape of the distribution of song lengths?
- The table of summary statistics does not give the interquartile range (or IQR) of this data set, but it does provide information that you can use to compute the IQR. Compute the IQR in the space below.
- The standard deviation is 58.71 seconds. How should this number be interpreted? In other words, what does the standard deviation tell us about this data set?
- The song that is at the 50th percentile is ___________ seconds long.
- From the histogram, we can see that approximately ________ songs are between 150 and 175 seconds long.
- The table of summary statistics shows us that the mean is larger than the median. Why do you think that is the case? In other words, what about the data might be leading the mean to be larger than the median? Please explain.
8. A histogram and a boxplot of the data are presented above. In your opinion, is one method of graphing this data a better choice than the other? Please explain.
9. In this data set, 25% of the songs are less than __________ seconds long and 75% of the songs are less than _________ seconds long.
- Which album has the least amount of variability in song length? Please explain.
- Which album has the most amount of variability in song length? Please explain.
- 75% of the songs on the ABR album are longer than __________ seconds.
- The song on the SPL album that is at the 25th percentile has a length of _________ seconds.
- From the boxplots, can you tell which album has the fewest number of songs on it? If you answer “yes,” tell us how many songs are on that album.
- The distribution of song lengths from the YSB album is skewed to the ______________ and the distribution of song lengths from the LIB album is skewed to the _______________.
- The table of summary statistics includes the median song length for each album, but not the mean song length. Consider the LIB album. Would you expect the mean song length to be less than the median song length, greater than the median song length, or equal to the median song length? Please explain.