Math 1040

Statistics and Data Collection

Statistics using tools to help us make predictions in our world to better understand and predict possible outcomes. It always beings with a Collection of Data. In this example we will view the possible statistical data outcomes that can come from a simple bag of skittles. Each student in the class purchased one 2.17-ounce bag of Original Skittles and recorded the following data in a table. My data can be found below.

Each students response was compiled into a list of responses to give our population data for the class, which can be found to the right in an excel formatted page.

This Qualitative data then gives us the means to organize and make some predictions towards the date and then see what the results to many questions that concern reading data.

My predictions on the proportion of each color we would see was based on a video I had once encountered that explained that companies add more yellow into the mixture to add appeal to the candy. My predictions for the proportion were as found in the table below.

The actual counts and proportions are found below. The data can also be found in a pie chart and bar graph found to the right.

Based of the data, I was very surprised by the data. I had originally thought that the data would be really close to equal or at least have a higher rise in the yellow color. But there also could be some biased or errors in the data (also known as lurking variables). Especially with the sample of 35 totaling to 382 skittles totals when the others were roughly around 60. We must consider that people could have bought the wrong sized bag, which can through of the data information. That being said with the information we do have, my proportions compared to the whole class(sampling population) were nearly the same. Both the green and purple were the low counts for the color.

What kind of sampling is this?

This type of sampling performed for the data is random sampling. Random sampling is sampling from a population. The population that we represent it Math 1040 class SLCC students. We are a small population, but we still are one. The sample is the colors of skittles we all randomly chose.

Excel Student Data

Graphs

Pie Chart- Colors of Skittles

Bar Graph- Colors of Skittles

Summary Statistics

The next thing we can do is look at the other information and data that can be calculated given the data from the skittles population.

The Skittles data has two different value ways that we can look at. It is qualitative and quantitative data.

What is the difference between qualitative and quantitative data?
Qualitative data is data that describes something, for example, skittles have qualitative data about what color they may be. They also have a quantitative data. We can ask this question by wondering how many totals are in a bag, or how many of one specific color is there.

What types of graphs make sense and what types of graphs do not make sense for qualitative data? For quantitative data? Explain why.
The best graph type to use for comparing colors of skittles percentages could be a bar graph. You could see the measure side by side to see the increases compared to each other. The best graph to use for quantitative data could be a dot plot. You would be able to see the values of the repeated total values. Or you could also use a box plot to help find the mean and outliners of the totals of skittles.

What types of calculations (eg. summary statistics) make sense and what types do not make sense for qualitative data? For quantitative data? Explain why.
The summary statics that does not make sense for qualitative data would be to find out the 5-summary statistics. The summary statics that don't make sense for quantitative data would be a pie chart. You would not be able to see the change in values the best and how they can rise and fall.

Looking at the graphs, we can also determine that the shape of “Total candies in each bag” is skewed right. This is not what I expected. I expected the levels to mostly be the same for the size of bag that everyone was purchasing. Looking at the graphs as well, we see there are outliers of the data. We have an outliner all the way at 382. I wonder if another size was accidently bought to produce that number. They change and affect the standard deviation of the data. It also affects the median to move over to accommodate the large data.

Confidence Intervals

With the data, we can also make inferences on what we can base statistics with a possible margin of error.
A confidence interval indicates that a percentage of all simple random samples of a sample size of the population whose parameter is unknown will result in an interval that contains the parameter. It also represents the expected proportion of intervals that will contain the parameter. It is also based off the point estimate.
Factors that affect the width of a confidence interval are critical values of the data sample because it produces a higher level of confidence. Other factors would be the margin of error as well because as it increases the confidence interval will grow as well.

Summary

Statistics involves information that will lead you to be able to make inference on situations that could lead to business success. It can help you to interpret sales and pitches from your favorite baseball player. The mean can provide you a lot of information. Also, graphs can have a lot of incorrect information to portray you to think incorrect data about the subject.

Reflection

This information will held me present future information for other classes. I have the means to make bar graphs and pie charts that will help visual show information that I have collected for the class. It will also help me portray, if for a study, what information can be inferred from my research.