When I was scheduling music for radio stations, I used a special software program called Selector. The goal was always the same: schedule a minimum number of songs (usually anywhere from 8 to 12 depending on the time of day) per hour, taking into account commercials, promos, imaging and announcer talk. This sometimes necessitated using blank slots in the schedules, placeholders that were assigned an arbitrary length of 3 minutes and 30 seconds, which seemed to me (and many other program and music directors) to be about the right average length of a song. That’s about as scientific as it got.
Today this email arrived.
Dear Mr. Cross,
We are AP Statistics students in high school. Recently, we read your article A Good Question: Why Are Songs on the Radio About the Same Length? We decided to test your claim that the length of the average song on the radio was 3 minutes and 30 seconds.
To do this, we took 360 random samples each from the top 40 charts of both rock and pop from the past 30 years. Separately, we calculated the means of these two categories. Using the calculation x±z*(σ/√n) = 246±1.96(44.7/√360)=(241.38, 250.62), we found with 95% confidence that the average pop song has a length between 4 minutes 2 seconds and 4 minutes 18 seconds.
In addition, using the calculation t=x-μ/(s/√n)=24/(44.7√360)=10.18 df=359 p<.00001, we found enough evidence to say that the average length of a pop song is greater than 3 minutes 30 seconds.
We did the same for the rock category, using the equations x±z*(σ/√n) = 244±1.96(52.9/√360)=(238.54, 249.46) and t=x-μ/(s/√n)=246/(52.9√360)=88.23 df=359 p<.00001 to find that the average rock song is between 4 minutes 1 second and 5 minutes 2 seconds long, and found enough evidence to say that the average rock song is greater than 3 minutes 30 seconds.
While our findings are significantly different from yours, it is possible that our sample was biased by year or by popularity. Regardless, we would like to thank you for the inspiration, and we hope that you find our conclusions as interesting as we did your article.
Emily Friedman and Isaac Santiago
That email wins the Internet for today. I stand corrected.