Professor Dr. M. Reza Zomorrodian
March 12, 2013
The following assessment investigates the practices involved in this semester’s statistical M&M evaluation. The paper initially describes the individual random samples taken and then combined into the class’ data set. Then the totals, their proportions, and some other descriptive statistics are detailed before examining the confidence intervals for the proportions. The next section tests the sample proportions against M&M’s advertized proportions. The final element of the project compares the percent of the Red and Brown candies in order to verify M&M’s claim of equality. The conclusion of the report offers recommendations for correcting any inconsistent proportions. Sweetening Statistics
Oddly enough, it was through the analysis of 1.69 oz bags of Milk-Chocolate M&M’s that made statistics my friend. Throughout the semester, the project used M&M’s to show many statistical principles in action. Each stage was simultaneously amusing and delicious. Not only was the project an ideal way to make statistics immediately understandable for anyone, it gave students the opportunity to use the hard-shelled candy analysis for more advanced elements in the course. Apparently, just like anything else, sweetening Statistics will in fact, make it more appealing.
Part 1 (Sampling)
In the initial phase of the project, each student’s individual responsibility ironically helped to increase the actual, very-collective objective of this phase, a single data set containing everyone’s results. The concepts of population, samples, and sampling methods learned from the first week’s text were reinforced by randomly selecting a bag from the display of three different stores. From each of the personally sampled bags, the different colors were then separated and inventoried within an excel file, which was subsequently submitted, combined with the others, and returned as the full random sample that would be used throughout the remaining stages.
Part 2 (Descriptive Statistics)
Equipped with the raw data from 69 bags of M&M’s, the second round offered the first taste of many of the more common statistical elements. To begin with, totals were collected from both the individual colors and all of the candies sampled. This data made it possible to determine the percentages of the colors currently available by dividing each color’s totaled figure by the tally from all 69 bags. The average numbers of candies per bag were also calculated by dividing the 3,852 candies sampled by the 69 bags evaluated.
A summary of the descriptive statistics was then ascertained based on the total numbers sampled, which included many calculations previously figured like the bags evaluated, the candies found to be in them, and the sample mean of 55.8 for each one. The most popular number of candies appearing in the bags, a.k.a. the mode, was 56, which was identical to the median number of 56 candies found to be in the middle of the 15-candy range between the minimum of 47 and the max of 62 candies found within one bag. And, according to the standard deviation, when the number found within the individual bags fluctuated from the usual 56, it was usually only by two.
Two of the descriptors, kurtosis and skewness, assisted in visualizing how the results would be displayed in the histogram, which was also created during this part of the project. The skewness measures symmetry, or in my case, the lack of it; and the high kurtosis advised of the peaked distribution.
Part 3 (Confidence Intervals)
Regardless of the measures taken to ensure a sample will be an unbiased representation of a population, there’s always a level of uncertainty when relying on such results. The third portion of this project addressed these concerns by quantifying the degree of uncertainty. By employing a 95% confidence interval of the color...