Mms Have Been Eaten Which Would Bring Our New Proportions Fo

75 Mms Have Been Eaten Which Would Bringournew Proportions For Each

75 M&Ms have been eaten, which would bring our new proportions for each color to: 12% Brown, 16% Yellow, 16% Red, 12% Blue, 24% Orange, 20% Green. Requirements: In a Word document, answer the following questions: How many M&Ms of each color were eaten? Based on our results, which color is the most favorite and which is the least favorite? How do you know? Which colors are higher, lower, or the same proportion as the website? Using Excel, construct a histogram with the frequency numbers of each color, ensuring appropriate labels. Paste the histogram into your Word document. Using Excel, construct a pie chart using the proportions from each color with proper labels, and paste it into your Word document. Answer questions about the charts: What do you observe? What is the shape and distribution? Compare these charts with those from your previous project, noting similarities and differences. Submit the Excel spreadsheet and the Word document.

Paper For Above instruction

In analyzing the eating patterns of M&Ms and comparing observed data with reported proportions, it is essential to quantify and interpret the data rigorously. The objective is to determine the number of M&Ms of each color eaten, identify the favorite and least favorite colors, compare observed proportions with the expected website proportions, and visualize the data through histograms and pie charts. Finally, analyzing these visual representations allows for insights into distribution characteristics and variations from expected proportions.

Calculating the Number of M&Ms of Each Color Eaten

Given the total of 75 M&Ms consumed, and the set proportions for each color, the actual count for each color can be computed by multiplying the total number by the respective percentage. Specifically, the calculations are as follows:

  • Brown: 75 × 12% = 75 × 0.12 = 9 M&Ms
  • Yellow: 75 × 16% = 75 × 0.16 = 12 M&Ms
  • Red: 75 × 16% = 12 M&Ms
  • Blue: 75 × 12% = 9 M&Ms
  • Orange: 75 × 24% = 75 × 0.24 = 18 M&Ms
  • Green: 75 × 20% = 75 × 0.20 = 15 M&Ms

These calculations indicate that exactly 75 M&Ms correspond to the proposed proportions, making it straightforward to interpret the distribution of colors eaten.

Identifying the Favorite and Least Favorite Colors

Based on calculated numbers, Orange is the most favored color, with 18 M&Ms eaten, representing 24% of the total. Green is the second most popular, with 15 M&Ms (20%). Conversely, Brown and Blue are the least favored, each with 9 M&Ms, accounting for 12% of the total. This analysis suggests preferences are distributed unevenly, with a clear peak in the orange category, potentially reflecting individual or cultural preferences.

Proportion Comparisons with Website Data

Comparing the observed counts with the expected proportions reveals how close the sample is to the expected distribution. For example, the observed proportion for orange (24%) exactly matches the reported value. Similarly, brown and blue are at the lower expected value of 12%. However, small differences in counts (e.g., 12 versus 9 M&Ms for brown and blue) highlight sampling variability.

Visualization: Histogram and Pie Chart Construction

Using Excel, a histogram can be constructed to display the frequency of each color. The histogram should include clear axis labels: the categories on the x-axis and the frequency of each color on the y-axis. This visual helps in understanding the distribution's shape; in this case, a skewed distribution with a peak at orange.

The pie chart, created with the proportions data, offers a visual representation of relative preferences, emphasizing how much each color contributes to the overall distribution. Properly labeled sectors and legend enhance clarity and facilitate comparisons.

Analysis of Charts and Distribution Characteristics

Observed histograms typically display the distribution pattern, indicating whether it is uniform, skewed, or bimodal. The pie chart complements this by illustrating relative proportions visually, with larger sectors corresponding to more favored colors. In this context, the distribution appears skewed towards orange and green, with smaller sectors for brown and blue.

Comparing these charts to previous data visualizations reveals consistencies in preferences or deviations due to sampling. For instance, in previous similar experiments, preferences might have favored other colors or shown more uniform distributions. Differences can arise from sample size, sampling method, or random variability.

Conclusion

The analysis of the M&Ms consumption data through quantitative calculations and visual representations provides clear insights into taste preferences. The dominant orange and green colors reflect individual preferences, while the smaller counts of brown and blue demonstrate lesser popularity. Visual tools like histograms and pie charts facilitate intuitive understanding of complex data patterns and distribution shapes. Such analyses are vital in quality control, marketing studies, and consumer behavior research, highlighting the importance of statistical visualization in interpreting real-world data.

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