Hey guys! Let's dive into some flower data today, shall we? We have a fascinating two-way table showing the distribution of roses and hibiscus flowers across three colors: red, pink, and yellow. It’s like a floral rainbow in spreadsheet form! Our mission? To analyze this data and figure out which statement truly captures the essence of these beautiful blooms. So, grab your metaphorical magnifying glasses, and let’s get started!
Understanding the Two-Way Table
First off, let's break down this two-way table. Think of it as a grid that helps us organize and understand information based on two categories. In this case, our categories are the type of flower (roses and hibiscus) and the color of the flower (red, pink, and yellow). Each cell in the table represents the number of flowers that fit both categories. For example, the cell where “Rose” and “Red” intersect tells us how many red roses we have. Got it? Great! Now, let's dive into the specifics.
Looking at the table, we can see the following:
- There are 40 red roses, 20 pink roses, and 45 yellow roses, totaling 105 roses.
- There are a whopping 80 red hibiscus, 40 pink hibiscus, and 90 yellow hibiscus, making a grand total of 210 hibiscus flowers.
- In total, we have 120 red flowers, 60 pink flowers, and 135 yellow flowers, summing up to 315 flowers in all.
This table is a goldmine of information! We can use it to compare the popularity of different colors within each flower type, or compare the distribution of colors across the two flower types. The possibilities are endless, guys! But remember, our main goal is to identify a true statement based on this data. So, let’s keep digging!
Analyzing the Distribution of Roses
Let's zoom in on the roses first. We have a total of 105 roses, and they come in three colors: red, pink, and yellow. The key numbers here are 40 red roses, 20 pink roses, and 45 yellow roses. Now, what can we infer from these numbers? Well, a crucial observation is that there are more yellow roses (45) than red roses (40) or pink roses (20). This immediately tells us something about the color preference within the rose category. It's clear that yellow is quite a popular color for roses in this dataset.
Another interesting point is the disparity between pink roses and the other colors. With only 20 pink roses, they are significantly less common than both red and yellow roses. This might suggest that pink is not as favored a color in the rose category, or perhaps there are other factors at play, like the availability of pink rose varieties. However, based purely on the data in the table, we can confidently say that pink roses are the least frequent among the roses.
To further analyze this, we can calculate the percentage distribution of colors within the roses. Out of 105 roses:
- Red roses make up approximately 38.1% (40/105).
- Pink roses constitute about 19% (20/105).
- Yellow roses account for roughly 42.9% (45/105).
This percentage breakdown reinforces our earlier observation: yellow roses are the most prevalent, followed closely by red roses, while pink roses lag behind. Understanding these proportions can be incredibly useful when comparing the rose distribution to that of hibiscus flowers. Are the color preferences similar across both flower types? That’s a question we can answer by examining the hibiscus data next!
Examining the Hibiscus Flower Data
Alright, guys, let's shift our focus to the vibrant world of hibiscus flowers! The table reveals that we have a total of 210 hibiscus flowers, distributed as follows: 80 red, 40 pink, and 90 yellow. Just like with the roses, we can immediately spot some interesting trends. The first thing that jumps out is the sheer number of yellow hibiscus – a whopping 90! This indicates that yellow is a highly popular color choice for hibiscus, even more so than for roses.
Looking at the other colors, we see 80 red hibiscus and 40 pink hibiscus. Here, we observe a similar pattern to the roses, where pink is the least common color. However, the difference between red and yellow hibiscus is more pronounced than the difference between red and yellow roses. This suggests that yellow is an even more dominant color in the hibiscus category.
To get a clearer picture, let’s calculate the percentage distribution for hibiscus colors:
- Red hibiscus make up approximately 38.1% (80/210).
- Pink hibiscus constitute about 19% (40/210).
- Yellow hibiscus account for roughly 42.9% (90/210).
Wait a minute... Those percentages look familiar, don't they? They're exactly the same as the percentage distribution for roses! This is a huge observation! It means that, despite having different total numbers of flowers, the proportion of each color is identical for roses and hibiscus. This is a key insight that we'll need to keep in mind when we evaluate potential statements about the data.
Comparing Roses and Hibiscus: Key Insights
Now, let’s put on our comparison hats and analyze the data across both flower types. We’ve already discovered one major similarity: the percentage distribution of colors is the same for roses and hibiscus. This means that, proportionally speaking, the preference for each color is consistent across both types of flowers. For every 100 roses, you'd expect roughly the same number of red, pink, and yellow flowers as you would for every 100 hibiscus flowers. That's pretty cool, right?
However, there are also some crucial differences. The most obvious one is the total number of flowers. We have 105 roses and 210 hibiscus flowers. This means that there are twice as many hibiscus flowers as roses. This is an important fact to remember, as it can influence the overall color distribution. While the proportions are the same, the actual numbers are different.
For example, while yellow flowers are the most common color in both categories, there are significantly more yellow hibiscus (90) than yellow roses (45). This is simply because there are more hibiscus flowers in total. Similarly, there are more red hibiscus (80) than red roses (40), and more pink hibiscus (40) than pink roses (20). Understanding this distinction between proportions and absolute numbers is vital for making accurate statements about the data.
Another insight we can glean is the overall color preference. Yellow appears to be the most popular color for both flower types, while pink is the least popular. This might reflect general aesthetic preferences, or it could be related to the specific varieties of roses and hibiscus included in the data. Whatever the reason, it's a clear trend that we can identify from the table.
Identifying the True Statement: Putting It All Together
Okay, guys, we've done a deep dive into the data, analyzing the distribution of colors within each flower type and comparing the trends across roses and hibiscus. Now comes the moment of truth: identifying the true statement. To do this effectively, we need to consider all our key findings:
- The percentage distribution of colors is the same for roses and hibiscus.
- There are twice as many hibiscus flowers as roses.
- Yellow is the most popular color, while pink is the least popular, in both flower types.
- There are more flowers of each color in the hibiscus category than in the rose category.
With these insights in mind, we can carefully evaluate any potential statements about the data. Let's imagine we are presented with some options. For instance, we might see statements like: