M&Ms®: Not Just Your Ordinary Candy Part 1 The first section of the project required students to purchase three random 1.69oz bags of M&Ms® from three different stores in an attempt to achieve as much of a random sample as possible. From that random sample, manual sorting was required to distinguish the various groups of candies by color and quantity. The colors identified from each bag were blue, orange, green, yellow, red, brown. Once established, the quantities for each color was documented from each student's sample and the individual samples where combined to create the full random sample used throughout the remainder of the project. The utilization of this full sample allowed each student the opportunity to use the same data instead of using individual data (which allowed the class to perform on one accord).
Part 2 The second section of the project required students to calculate the mean, standard deviation, proportions and determine the type of histogram that resulted from the data retrieved. The mean or average, according to Larson & Farber (2009) is defined as “the sum of the data entries divided by the number of entries” (p.67). The sample mean of each bag of M&Ms® for this project was found by adding the total number of candies (7563) in each bag (x) and dividing by the total number of 1.69oz bags of candy (135). The standard deviation, according to Larson & Farber (2009) is defined as the “sample data set of n entries is the square root of the sample variance” (p. 84-85). The standard deviation of the total sample basically tells how wide spread the sample data is. The larger the standard deviation is, the wider spread the data is. The total number of candies for each color (x) is displayed in the chart below. Because the total sample number of candies was 7563, the proportion of each color candy was calculated by dividing the individual number of candies (by color) by the total number of candy. The proportions are merely the percentages of each color is contained in each bag. For example, the percentage of blue M&Ms® for our sample is 22.65%, orange is 22.27%, etc. The calculations for the proportions are displayed (by color) below for your review: As one can see, the results of the sample indicate that there are a greater percentage of blue M&Ms® candies in each bag (which comprised of 22.65% of the total sample), followed by orange, green, red and yellow. The least proportioned color in the sample was brown (which comprised of only 12.5% of the total sample). Because of the results of the data, the associated histogram yields neither a left- or right-skewed histogram but, rather, a symmetric histogram.
The third section of the project required students to calculate the confidence interval for each candy color in the sample. Larson & Farber (2009) define a c-confidence interval as an interval estimate of a population parameter such as µ (p. 313). In order to calculate the confidence interval, the margin of error also had to be computed. The margin of error “(sometimes called the maximum error of estimate or estimate tolerance) E is the greatest possible distance between the point estimate and the value of the parameter it is estimating” (Larson & Farber, 2009, p.312). Bluman (2006) states that the maximum error of estimate “is the maximum likely difference…