Question

The color distributions for two snacksize bags of \(\mathrm{M\&M}^{\prime} \mathrm{S}^{@}\) candies, one plain and one peanut, are displayed in the table. Choose an appropriate graphical method and compare the distributions. $$ \begin{array}{lrrrccc} & \text { Brown } & \text { Yellow } & \text { Red } & \text { Orange } & \text { Green } & \text { Blue } \\ \hline \text { Plain } & 15 & 14 & 12 & 4 & 5 & 6 \\ \text { Peanut } & 6 & 2 & 2 & 3 & 3 & 5 \end{array} $$

Short answer

Question: Compare the color distributions between plain and peanut M&Ms using a graphical method. Describe the key differences found within these distributions. Answer: By using a side-by-side bar chart to compare the color distributions, we can conclude that the distributions are not the same for plain and peanut M&Ms. Plain M&Ms have a higher count of brown, yellow, and red candies, while peanut M&Ms have a higher count of blue candies.

Step-by-step solution

Prepare the Data for the Graph

Organize the given data into a table that provides a clear comparison of the two M&M types. | Color | Plain | Peanut | |:---------:|:-----:|:------:| | Brown | 15 | 6 | | Yellow | 14 | 2 | | Red | 12 | 2 | | Orange | 4 | 3 | | Green | 5 | 3 | | Blue | 6 | 5 |

Create the Side-by-Side Bar Chart

Using the data table, plot a side-by-side bar chart with colors on the x-axis and the number of candies on the y-axis. Color the bars according to the M&M color, and label each bar with its corresponding value.

Analyze the Chart

Look at the side-by-side bar chart and compare the distributions. Observe the trends and differences between the plain and peanut M&Ms. For example, the plain M&Ms have more brown, yellow, and red candies, while the peanut M&Ms have more blue candies.

Interpret the Results

Based on the side-by-side bar chart, we can conclude that the distributions are not the same for plain and peanut M&Ms. There are significant differences in the number of candies for each color in the two types of M&Ms. For example, plain M&Ms have a higher count of brown, yellow, and red candies, while peanut M&Ms have a higher count of blue candies.

Key concepts

Bar Chart

A bar chart is an excellent choice for visually representing categorical data like the color distribution of M&M candies. It is straightforward, offering clarity in the comparative analysis of different categories. The x-axis represents categories—in this case, the color of the candies. The y-axis quantifies the data—for instance, the number of candies of each color.

In our example, a side-by-side bar chart is employed. Each color has two distinct bars: one for plain and another for peanut M&Ms. These bars stand side-by-side, making it easy to see and compare the quantities directly. The visual clarity provided by this method helps in identifying which types of M&Ms dominate in particular colors.

Keep in mind, when creating bar charts, it's essential to align the y-axis to 0 to avoid misleading comparisons. Consistent spacing and labeling make a bar chart easier to read and understand.

Comparative Analysis

Comparative analysis involves evaluating and comparing datasets to draw insightful conclusions. In the context of M&M colors, this technique allows you to see which colors are more prevalent in each type of candy. This becomes particularly useful in understanding preferences or manufacturing processes.

For our side-by-side bar chart, the comparison is straightforward. By observing the height of the bars, you can quickly determine which M&M type has more candies of each color. For instance, the plain M&Ms clearly outrank the peanut M&Ms in the number of brown, yellow, and red candies. Meanwhile, peanut M&Ms have a slightly higher count of blue candies.

• Identify dominant categories: Which color is more prevalent in your dataset?
• Spot trends: Are there colors that consistently appear more in one type of M&M?
• Consider scale: Ensure both datasets are on the same scale for a fair comparison.

By conducting this analysis, not only can we identify differences, but we can also speculate potential reasons such as manufacturing choices or consumer preferences.

Color Distribution

Understanding color distribution in M&M candies provides insights into how different candy types might be produced or marketed. Each color's frequency gives clues about the candy's composition.

In our example, the color distribution shows that plain M&Ms have more brown, yellow, and red candies compared to their peanut counterparts. This could suggest that these colors are favored in the production or marketing of the plain variants. On the flip side, blue appears more frequently in peanut M&Ms, hinting at a marketing tactic or flavor association.

• Frequency: How many times does each color appear? This helps identify which colors dominate.
• Diversity: Which type offers a more varied color palette?
• Consumer appeal: How might these color choices affect consumer perception?

Analyzing color distribution is not just about counting; it's about understanding strategic decisions. It provides a visual and quantifiable metric that can influence production, marketing, and even sales strategies.