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The Skittles data for the variable of “Total Candies in Each Bag” was a little surprising. I expected the data to be bell shaped, but this data seems to be skewed a bit left. It’s not skewed by much, in fact, only .5! In a data set that is skewed left, the mean is typically less than the median. Our mean (58.6, but we round up to a whole number) and our median for the class data is 59, and we had a standard deviation of 2.4. Our five number summary appeared as below:

49  58 59  59.5 63

 

Five number summaries are a great way to interpret our data. These number summaries can be easily incorporated into boxplots that help us visualize the data. After looking at the five number summary, I had a good idea of what our boxplot for this data set was going to look like. I think that visualizing box plots is a lot easier than histograms, and that when using frequency data, they might be the best bet for visual representation.

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Our histogram data, on the other hand, was not exactly what I expected. I did expect it to semi bell shape and skewed to the left, but in all actuality, it wasn’t that helpful at visually representing the data. If I wasn’t enrolled in a statistics class, I think it would be a lot more difficult for me to recognize the mean, which was 59. You also can’t pinpoint the median or the the five number summary looking at the histogram. I always thought data was best represented on a histogram, but after using boxplots for this project I have completely changed my mind. 

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Qualitative data describes individuals by characteristics that are descripted, not measured. This information is used to classify or categorize the data, and can be measured by frequency in a frequency distribution. We categorized our data for the Skittles project by color- red, yellow, green, purple, orange- and then measured the frequency of each occurrance in each bag of Skittles. Graphs that would work well to display this type of data would be bar graphs, histograms, and pie charts. These would work well because they can display the frequency and relative frequency of the data. Graphs that wouldn't work well are box plots or graphs that focus on measures of spread. Summary statistics that would apply to qualitative data would be the mode, median and the minimum. The mode would point out which color occurred the most, and minimum would point out which occurred the least. The median would be the number of occurrance that were in the midline of the data. The mean and standard deviation and quartiles wouldn't make sense with qualitative data because they are measures of spread. 

Quantitative data is data that is represented numerically by measurable values. For example, the totals of each color of Skittles in each bag. We can organize this data into a variety of different graphs. Most graphs would work to accurately display this data. All of the summary statistics would work for this data because we could measure the spread between each bag of skittles. We could use the mean to say, on average, a bag of Skittles has X red Skittles, for example. We could also use standard deviation to see if we had any bags of Skittles that were particularly "off", or had outliers in their data.