First to get started with the project three 1.69 ounce bags of plain M&M’s were purchased from Shoppers, and 2 7-11’s. These bags will help with taking a sample of the population that is produced. Purchasing the bags from three different stores will help with the results of the project being meaningful because it is assured that the samples will be truly random. Random sampling is when all members of a group have an equal and independent chance of being selected. Next each individual bag of candy was opened and counted. When counting the candies were put into groups based on their color (blue, orange, green, yellow, red and brown) and the results were recorded on a spreadsheet. Once every bag was counted the findings were added up to find the total number of candies within each of the three 1.69 ounce bags of plain M&M’s. The findings were as followed: Bag One had 54 candies, Bag Two had 57 candies and Bag Three had 56 candies.
For this part of the project all of the data findings from the class were combined into one class data set. The data focused on the color proportions and the number of candies per bag. The information that was used for the color proportions is the total for each color and the total number of candies sampled. The data in the number candies in bag column was used for the number of candies per bag.
First the sample proportions for each of the colors were calculated. A sample proportion is the number of individuals in the sample with a specified characteristics divided by the sample size. For this particular project it was done by adding up each color column and the numbers of candies per bag column individually to find the sum of each column first. Then to find the sample proportions the total number of the specific color candies from all the bags was divided by the total number of candies in all the bags. This step was repeated and completed for each of the colors. The results are shown in the chart below (the total number of candies are depicted by
‘x’ and sample proportion is depicted by ‘p’).
The sample mean was then calculated. To find the sample mean the mean of the number of candies in bag column was computed. The sample mean was 55.93442623. Then using
Microsoft Excel a histogram for the number of candies per bag was created, descriptive statistics for the total number of candies per bag was computed and lastly a summary was created. A histogram is a bar graph that represents the frequency of a data set. Descriptive statistics show the mathematical quantities (mean, median, standard deviation) that summarize and interpret some of the properties of a set of data sample.
The summary summarized the sample proportions, sample mean, sample standard deviation, histogram description and the sample sizes of this project. The sample standard deviation of the mean number of candies per bag was 1.7211. The histogram had a Skewed Left
Distribution which means that is negatively skewed because the tail extends to the left and mean is to the left of the median. The distribution had two possible outliers which are 60 and 62.
Outliers are data entries that are far removed from the other entries in the data set. Sample sizes of the project were the total number of candies sampled (3412) and the total number of bags sampled (61).
This part of the project dealt with constructing confidence intervals for the proportions of each color and the mean number of candies per bag as