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Owner: 10schnb
Created: Sep 21, 2009
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M&M Count in Fun Size Packages
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The distribution of the amounts of M&Ms in fun size packages (2009) has a roughly skewed left shape. The data shows range from 16 to 20 and an IQR of only one; both of these measures of spread show that the distribution has very little variability. The min, 16, is an outlier. The distribution is not symmetrical enough to justify the mean and std. deviation as a good summary, so the five number summary (16, 18, 19, 19, 20) is a good indication for this distribution.

It is important for the M&M count in fun size packages to have this low variability. From a consumer standpoint, a person would want to know for sure that they will always get nearly the same amount of M&Ms in every package, and not get an unreasonably low quantity. From the manufacturer's view, the M&M manufacturer would not want too many M&Ms in each package, or else it would cost the company money if it happened too often. For these reasons, it is important that a regular quantity of M&Ms is in any given fun size package, with very little variability. However, to acheive a zero level of variability would be very difficult. To do this, the current machines that sort M&Ms would most likely need updated, and the workers would have to pay much stricter attention than currently to ensure that every package was the same. Even so, error is always possible and it is thus unlikely that a zero variability level is possible.

The distribution of yellow M&Ms has a slightly different shape than the M&M counts as a whole. One may call the distribution of yellow M&Ms symmetrical, perhaps with a slight skew to the right. In general, the number of yellow M&Ms is much lower than the total; this is obviously because there are six possible colors of M&Ms that could be in any given package(a median of 4 compared to 19). Also, the yellow M&Ms have much more variability, with a range of 8 compared to a range of 4. This difference is significant; it is less important what color the M&Ms in a package are, as long as there is a reasonably small range of quantities that are accepted for the package as whole. For example, the manufacturer would not be careful to make sure that there was always the same amount of yellow M&Ms, since yellow M&Ms are no different from other colors in taste. The manufacturer would, however, want to keep an eye on how many total M&Ms there were in every given package.

The distributions of 2008 M&M counts and 2009 counts show differences in shape, center, and spread. The histogram of 2008 M&M counts shows s fairly symmetrical shape, compared to the slightly skewed shape of the 2009 counts. Also, the spread of  the 2008 individuals is slightly larger than the 2009 individuals (a range of 6 compared to 4) but with the same small IQR of 1. Notice also that the 2008 data set had 2 outliers while the 2009 set had only one. As far as the center goes, the 2008 data had a significantly higher center (median of 21 compared to 19). Notice also that the lowest value in 2008, which was also an outlier, is the same as the median for the 2009 distribution. This proves that in 2008, the M&M manufacturers allowed for both a higher median amount of M&Ms as well as slightly more varibaility in the amount of M&Ms in each package.

Result 1: M&M counts Column Statistics   [Info]
Summary statistics:
Column n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3
2009 counts 25 18.36 1.1566666 1.0754844 0.21509688 19 4 16 20 18 19

Result 2: M&M 2009 Histogram   [Info]
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Result 3: 2009 M&M Boxplot   [Info]
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Result 4: yellow M&M Histogram   [Info]
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Result 5: 2008 M&M Histogram   [Info]
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Result 6: 2008 to 2009 M&M comparison Boxplot   [Info]
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Data set 1. M&M fun-size counts 2009   [Info]
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