# Popular Music/Beliebers and Probability

Justin Bieber has had a huge international following since his rise to stardom in 2007. He has over 255 million Instagram followers and 114 million Twitter followers as of September 2022. The concepts of being a "Justin Bieber fan" or being a "Justin Bieber hater" are frequently discussed by today's music fans. Given how prevalent these topics are, you would seriously think that someone, somewhere would have conducted a survey to find demographical information about the Justin Bieber fans, or Beliebers. How many Justin Bieber fans are there? What fraction of the Justin Bieber fans are female? In a perfect world, the answers to these two hotly discussed questions would be readily and easily accessible on the web. Sadly, we don't live in a perfect world, and reality is harsh sometimes. Even so, after some digging and some trial and error with several different search queries, I could find at least two news articles that can be used as clues to find the ballpark and magnitude of the fan club's size.

## Number of Beliebers in the US (April 2014)

In the week of April 7-11, 2014, several news outlets reported the prevalence of "Bieber fever" in the United States. A Huffpost article, dated April 8, 2014, published the results of an Estately survey that was used to find the Belieber proportions in the states and the Canadian provinces. The people who conducted the survey were kind enough to give the percentages down to hundredths of a percent. All 50 states ranged between 6% and 10%. Washington State had the lowest percentage of Justin Bieber fans, at only 6.82%, while Rhode Island had the highest percentage (9.33%). Rhode Island is tied with Wisconsin at 9.33%, and Alabama is not far behind (9.23% of Alabama's residents are Justin Bieber fans). Although April 2014 is a long time ago in the context of Justin Bieber and his timeline as a famous star, a string of news articles that are generous enough to give precision on the level of 10$^{−4}$ is way too good to pass up. And hey, given the shortage of online information about statistics of Justin Bieber fans, I'll take what I can find.
Using the information in the above paragraph, since the minimum was 6.82% and the maximum was 9.33%, that means the overall percentage was somewhere between 6.82% and 9.33%. Using the fact that the U.S. population was 318,400,000 in 2014, we can multiply this number by 6.82% and 9.33% to see that the Justin Bieber fan population was somewhere between 20 million and 30 million.
318,400,000 × 0.0682 = 21,714,880
318,400,000 × 0.0933 = 29,706,720
Now that the US population is considerably higher than it was eight years ago (today it is around 330 million), and the 2015 Purpose album converted many people into fans (evidence to be given shortly), the true numbers as of 2022 are presumably considerably higher than they were in 2014. While we don't have information on how many non-fans converted to fans, a December 2015 by the Business Insider stated that Bieber's "new dance-pop sound — a genre called 'tropical house,' which is a mix of electronic dance music and Caribbean vibes — has grown men that had never even heard of Bieber before falling in love with his music." Again, no specific numbers on how many or what percent, but large enough for Business Insider and several other news outlets around that time to say that adult males are a "new audience" for Justin Bieber thanks to his new album.

## Gender Demographics (February 2011)

On February 14, 2011, the Weekend Box Office reported that the audience for Justin Bieber's Never Say Never movie was 84% female. This ballpark is reinforced by several other news articles about concerts in 2010, 2011, and 2012. A November 2012 concert was reported to be 85% female, while other concert articles gave 80% and 90% as "round number" estimates.
A Visual.ly presentation titled, "If Justin Bieber Fans Were a Country", gave the gender distribution as 21% male and 79% female. I couldn't find a date for the page, but a graph on the page shows April 2010, September 2010, February 2011, and November 2011, so this page was likely created sometime in 2012 or December 2011. If someone can find a more precise date, please let me know on the discussion page. External links are also useful, though due to Wikibooks edit filters, you will need to be signed in to add links to any Wikibooks page.

## Round numbers

For the rest of this page, I will use the following figures:
* 25 million Beliebers
* 10% male, 90% female
Until I find evidence to the contrary, I will assume that there is no correlation between name and being a Belieber. If a correlation is found, I will assume that it is due to gender or age, and not the name itself. For example, a study would undoubtedly find that "John" is less likely to be a Belieber than "Sarah", but that is only because John is almost always a boy's name while Sarah is almost always a girl's name.

## First names

If a first name exists and it is within the top 1000, you can bet your life savings that there is a Justin Bieber fan with that first name somewhere in the United States. For sufficiently popular names, a follow-up question is How many should we expect?
Assuming 25 million Beliebers with a sex ratio of 10% male, 90% female, we can expect roughly 2,500,000 males and 22,500,000 females.
Roughly 3.2% of males in the United States are named John, and 2,500,000 × 0.032 = 80,000.