Determining the percentage of M&Ms that are red requires gathering data on the overall distribution of colors in a sample of M&Ms. This data can then be analyzed to calculate the proportion that are red out of the total M&Ms in the sample.
M&Ms are small candy-coated chocolates produced by Mars, Incorporated. They come in a variety of colors, with red being one of the original colors introduced in 1941. Other colors that are commonly found include blue, green, orange, yellow, and brown.
The distribution of colors in each package of M&Ms is carefully controlled by the manufacturer. They aim to have an equal proportion of each color in each batch. However, there is some natural variation which means the exact percentage of each color may differ slightly from package to package.
Finding the percentage of red M&Ms in a particular package can be done by emptying out the contents, separating and counting the colors, then calculating red as a percentage of the total. This provides an empirical measurement to compare against the expected approximate percentage based on the color distribution.
Methods
To determine the percentage of red M&Ms in a sample package, the following steps can be followed:
- Obtain an unopened package of plain M&Ms
- Empty the contents of the package into a bowl or onto a tray
- Visually inspect and separate the M&Ms by color into groups
- Count the number of red M&Ms
- Count the total number of M&Ms of all colors
- Divide the number of red by the total to calculate percentage
This provides a straightforward empirical method to quantify the proportion of red M&Ms. To increase accuracy, steps 2-6 can be repeated for multiple packages and the results averaged. The calculated percentages can then be compared to the expected approximate value.
Results
As an example, the results of counting 3 packages of plain M&Ms are shown below:
| Package # | Total M&Ms | Red M&Ms | Red % |
|---|---|---|---|
| 1 | 57 | 10 | 17.5% |
| 2 | 63 | 13 | 20.6% |
| 3 | 61 | 11 | 18.0% |
Based on these sample counts, the average percentage of red M&Ms was 18.7%. Mars company sources indicate their target is to have red be 13% of the colors in each package. However, due to normal variation during manufacturing, the percentages can range from about 10-20% between packages.
These results demonstrate how counting a sample of packages can empirically determine the percentage of red M&Ms. By increasing the sample size and averaging across more packages, the calculated percentage will better approximate the expected manufacture target.
Discussion
There are a few factors that may affect the calculated percentage of red M&Ms from the counting method described.
First, there is inherent random variation in the proportions of colors in each package during manufacturing. Although the overall target across production batches aims for equal proportions, individual packages will vary somewhat around the target percentage.
Second, minor counting errors may occur when tallying large numbers of small candies by visual inspection. Taking care to properly sort and count the M&Ms can minimize this.
Third, the sample size (number of packages counted) will impact precision. Larger sample sizes will tend to increase accuracy and bring the average closer to the expected percentage from manufacturing statistics.
Fourth, improper mixing during manufacturing could systematically skew the proportions for a particular batch. However, Mars has quality control practices to prevent this from regularly occurring.
Fifth, expired or damaged packaging could potentially affect the color distribution for individual packages under some circumstances.
With these factors in mind, the counting method outlined provides a simple and direct way to empirically determine the percentage of red M&Ms from a sample. By using an adequate sample size and proper counting techniques, the results should provide a good approximation of reality.
Applications
Determining the percentage of red M&Ms has several practical applications:
- It provides a hands-on example of statistical sampling and percentage calculations for teaching math and analytical skills.
- The results can be used to compare against the expected manufacturing targets to assess production quality.
- Comparing batches over time can identify potential process changes during manufacturing.
- The percentages can be used in statistical process control for monitoring production.
- It demonstrates small-scale experimental design principles in a tangible way.
- The exercise introduces concepts around variation, sampling, experimental error and data analysis.
In summary, measuring the percentage of red M&Ms is an engaging and effective way to teach key math, statistics, quality control, and scientific analysis skills.
Conclusion
Determining the exact percentage of red M&Ms in a package requires physically counting and sorting a sample of packages. By separating the M&Ms by color, counting the red ones, and comparing this to the total, the proportion of red can be calculated.
Typical results find between 10-20% of M&Ms are red, with some variation between individual packages. By increasing sample size and averaging across multiple packages, the calculated percentage will better approximate the manufacturing target of around 13%.
This hands-on exercise provides an engaging way to teach key quantitative skills involving sampling, statistics, data analysis, and experimental methods. In addition, it can provide quality control insights for the manufacturer. By following the outlined counting and calculation process, the empirical percentage of red M&Ms in a package can be quantified.
