# Mathematical Statistics Project

In short, the whole purpose of this project was to learn more about bell graphs. Now it's more complicated than that, of course. To add a social element, we had the idea to graph the ratings that different age groups in our school give to different musicians of different times, to try to find the bell curve for different ages.

We chose this research option because we were curious about other peoples opinion on certain artists or bands. I, specifically, was hoping to find a correlation between the criticism and reception of certain bands, and public opinion on them. Which leads directly to my hypothesis:

### "Common criticism for modern music is directly related to the public opinion, and vise versa."

For our groups data collection method, we chose to use the stratified sampling method, which means that we would classify certain people into groups before interviewing them, separate from others. For this project, we will be classifying people into groups dictated by their grade level.

Our group has agreed to different Artists or musical groups, and different varying grade levels to accompany them. I personally chose to use a system of data collection that used a graph. On this graph, I would create a system where people would put their age, grade, and preference for my chosen bands, which were Taylor Swift and Daft Punk.

When surveying 12th graders, the results were as follows:

For Daft Punk: (On a scale of 1 to 10)

9, 8, 1, 0, 0, 9, 7, 6, 4, 10, 10, and 7.

For Taylor Swift: (On a scale of 1 to 10)

0, 6, 10, 8, 0, 0, 2, 8, 10, 0, 0, and 5.

When surveying 6th graders, (this time in Survey Monkey) the results were as follows:

For Daft Punk:

For Taylor Swift:

Then, the results in bar graph form (respective order.)

Of these numbers, additional information follows:

#### For the 12th grader report on Daft Punk:

Median: 7. Mode: 0, 7, 9, 10. Average: 5.91666

#### For the 12th grader report on Taylor Swift:

Median: 3.5. Mode: 0. Average: 4.08333

#### For the 6th grader report on Daft Punk:

Median: 6,5. Mode: 0, 10. Average: 5.5

#### For 6th grader report on Taylor Swift:

Median: 6. Mode: 2, 7. Average: 5.5.

The average of *all* the averages was about 5.16666, which makes the ultimate standard deviation equal 3.644111003 for all the graphs combined. From this, I gathered that the majority of people that I surveyed were incredibly cynical, yet the average change from highest to lowest score was supprisingly small.

I noticed, with some dismay during the survey, that results contradicted my estimations. Rather than completely extreme results, the results were rather mixed. On average, about half the people interviewed liked either band, and about half disliked said band, for all situations. There appeared to be little difference in results between genders or grade levels during the survey, and the only strange thing that occurred was the extreme standard deviation value of 3.64111003. This was because most of the answers submitted were either 10 or 0, making both numbers the mode on many occasions.

Hopefully, further research can be completed with a more diverse audience to try to get a more accurate result, which is exactly why we have my friend, Dylan Tagg. You can see his Digital Portfolio here.

His website displays the following:

"Collecting data was easy for my sampling method. My method was random sampling then I choose the results for each grade level I choose which would be clustered sampling. I choose this method because it would be the most efficient and effective."

His statistics ran as such:

Green Day

Mean:4.8 Median: 6 Mode: 5 and 6 Outlier: 10

Justin Beiber

Mean:3.4 Median: 3 Mode: 3 Outlier: 10

His numbers show a lower average than mine, but share the similar trait of having the outlier of 10, and the median of 3 and 6-ish. He explained in his writings how he shared the similar trait of having more people give the popular artists either a very high score or a very low score, while the less popular artist received a score in the middle range.

Later, I got Dakotas data. His information can be found here.

His information showed how, strangely enough, that both his bands (One direction and Fall out boy.) had similar medians for both his results, 5 and 6. He shared the same mode too, with 0 being the most common number.

It has thus been concluded by me that the only logical statement that can be made of this is that while mainstream opinions may be drastically different, when you look at the data and compare it with other tests of similar subject, then the difference is really only about 2 or 2.5 units off. So, perhaps mainstream opinion is drastically exaderated?