Statistics

The following is a semester long group project. The first part is a random sample of skittles bags. Each member of my class was to go out and purchase a bag of skittles. We then tallied the number of skittles for each of the following colors: Red, Orange, Yellow, Green, and Purple. The first column is the number for each individual bag. The last column is the total number of skittles in each bag, and the columns in the middle are the totals for each color. We then calculated the five number summary for our data. We found that we had a minimum number of skittles per bag of 37, a maximum of 94, our mean number of skittles was 58.57, and a standard deviation of 7.12. We then calculated the totals of each color and found percentages of each color as well. We were surprised to see that our percentages were not what we had guessed. We predicted that there would be an equal percentage for each color of 20%. Instead we got 20.7% for Red, 21.9% for orange, 20.2 for yellow, 19.1% for green and 19.7% for purple. We also created a pie chart and pareto chart for our findings.

After creating our five number summary and the above graphs we moved on to the next part of our group project: summary stats. We explored different types of graphs and the information they could provide us. We discovered that instead of writing out the five number summary, as I have done above, we could use a visual representation of the data. The box plot below not only gives us the same five number summary, it also give us any outliers. We were able to find the upper and lower fences of our data. Any points outside of our fences were considered outliers. The lowest three skittle bag totals happened to be outliers, as well as our two highest bag totals. Those are represented by blue points on the box plot. We also created a frequency histogram. I believe that these two types of graphs are quick and easy ways to both explain and understand data. I much prefer the visual aspect of a graph over that you recieve from a written summary. I also think it enables us to get a better idea of how the data is distributed. These graphs were a useful tool in summarizing and interpreting our data. 

Lastly, we learned to create confidence intervals. These confidence intervals allowed us to take our sample of 45 different bags of skittles and make fairly confident conclusions about the entire population of skittles bags. It would be immpossible for our class to go out and count how many candies are each and every bag of skittles. Instead, we take a random sample and make educated gueses about the whole population based on the results from our sample. The confidence intervals also enabled us to give a certainty, such as 95% certain, about the data we reported. For instance, when trying to find out how many yellow candies are in each bag of skittles, we were able to find that there was between approximately 57 and 60 yellow candies in each bag of skittles. We were also able to report that with a 95% certainty. This gives our audience a greater assurance of the accuracy of the numbers we provided them. 

Heather Murray

Group Project Part 5

7/23/19

 

Over the course of this project I’ve learned how statistics goes beyond the class and can be applied in a real world setting. Using statistics to maximize production in a business, such as a candy company, is one example of how statistics can be applied in a manner very similar to our skittles project. Statistics can help you identify overweight candies with mean confidence intervals. Say, for instance, a company is producing 60 pounds of candy a day. However, their sales only account for 50 pounds of product a day. If the unaccounted 10 pounds of daily product is actually due to overweight candies, a mean confidence interval would be able to help them identify this problem. It would show them the range of average candy weights for their candies, exposing the fact that, for example, 40% of their candies are 0.1 gram overweight. Once they were able to identify the problem, they could then correct it by changing the way they produce candy so as to not make overweight candies, thus, increasing profits.

Another way that this project will benefit me in the future is by allowing me to analyze my finances. I can better compare interest rates when deciding who to invest with my money with and also when applying for a home loan. If I need to save money, I could better identify areas to limit my spending by computing the average amount of money I spend on eating out, pleasure shopping, and entertainment. I could then compare the monthly averages for each of the afore mentioned categories and identify the category I spend the most money in, and then limit myself in that category. I could set a goal of reducing spending in that category by 25%. I could then continue to track my average monthly spending and reduce my frivolous spending and save money to be used in a more meaningful way.

I’ve always enjoyed statistics. I love that we have access to all the SLCC databases, which is a place where I can really dig into real life statistics. I really enjoy looking up statistics on diet, vaccines, exercise, education, and many other random categories I’m interested in. I realize my views may be considered controversial by many, however, after looking into the statistics on vaccine injuries I was able to make a more educated decision when deciding what vaccines to give my children. Before I had this information, I felt like I had no choice in the matter. Being armed with the knowledge that my child has the same chance—about 1 in 10,000—to be severely affected from catching measles (this was during the recent measles outbreaks) as they would from receiving anesthesia in the hospital, and then comparing that to the approximate 1 in 900 children who have an abnormally adverse reaction to the Measles Mumps and Rubella (MMR) vaccine, I was able to make the right decision for my child in that matter. Had I not been able to compare the statistics I probably would have allowed my family to pressure me into giving my, then, 9-month-old son the MMR vaccine 3 months before the doctors recommended. Statistics have and will continue to be a useful tool for me to use in all kinds of situations.