Decoding Shirt Statistics Calculating The Probability Of Picking A Medium Shirt

Hey guys! Ever stumbled upon a table of data and felt like you're staring at a cryptic puzzle? Well, today, we're going to break down a shirt inventory table and answer a crucial question using the information it holds. This isn't just about numbers; it's about understanding how data can help us make informed decisions. So, buckle up, and let's dive into the fascinating world of shirt statistics!

Understanding the Shirt Inventory Table

To kick things off, let's take a closer look at the table we're dealing with. This table presents a breakdown of shirts by color (Red and Blue) and size (Large and Medium). Think of it as a snapshot of a shirt collection, neatly organized for easy analysis. We've got three key categories here: Color, Size, and Total. The Color column tells us the different colors of shirts available, while the Size column categorizes them into Large and Medium. The Total column, as you might guess, gives us the total count for each combination of color and size, as well as the grand total of all shirts.

The table is structured like a grid, with rows representing colors and columns representing sizes. At the intersection of each row and column, you'll find the number of shirts that match that specific color and size. For example, the intersection of the 'Red' row and the 'Large' column shows us how many large red shirts we have. The beauty of this table lies in its simplicity and clarity. It allows us to quickly grasp the distribution of shirts across different categories, making it easier to answer questions and draw conclusions. But why is this important? Well, imagine you're running a clothing store, and you need to decide which shirt sizes and colors to restock. This table can be your best friend, guiding your decisions and ensuring you don't run out of popular items. Or perhaps you're just curious about the composition of your own wardrobe! Whatever the reason, understanding how to read and interpret this table is a valuable skill.

Breaking Down the Numbers

Now, let's get down to the nitty-gritty and dissect the numbers in this shirt inventory table. We'll go through each cell, explaining what it represents and how it contributes to the overall picture. Starting with the red shirts, we see that there are 42 large red shirts and 48 medium red shirts. Adding these two numbers together gives us a total of 90 red shirts. This is a crucial piece of information because it tells us the total number of red shirts available, regardless of size. Moving on to the blue shirts, we have 35 large blue shirts and 40 medium blue shirts, totaling 75 blue shirts. Notice how the table neatly summarizes the data for each color, making it easy to compare the quantities of red and blue shirts. This is particularly useful if you want to quickly identify which color is more prevalent in the inventory.

But the table doesn't stop there. It also provides totals for each size category. Looking at the 'Large' column, we see that there are 42 large red shirts and 35 large blue shirts, giving us a total of 77 large shirts. Similarly, the 'Medium' column shows 48 medium red shirts and 40 medium blue shirts, totaling 88 medium shirts. These totals are valuable because they allow us to understand the size distribution of the shirts. For instance, we can see that there are slightly more medium shirts than large shirts in the inventory. Finally, the bottom-right cell of the table shows the grand total of all shirts, which is 165. This number represents the entire sample space from which we'll be picking a shirt at random. It's the denominator in our probability calculation, and it's essential for answering the question we're about to tackle. Understanding these individual numbers and how they relate to each other is the key to unlocking the insights hidden within the table. So, with this foundation in place, let's move on to the main question and see how we can use this data to find the answer.

The Question: Probability of Picking a Medium Shirt

Alright, guys, let's get to the heart of the matter! The question we're tackling today is: If you pick a shirt at random from the given batch of 165 shirts, what is the probability of selecting a medium shirt? This is a classic probability question, and by understanding the data in our shirt inventory table, we can solve it with ease. The keyword here is probability. In simple terms, probability is the measure of how likely an event is to occur. It's expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain. In our case, the event we're interested in is picking a medium shirt. To calculate the probability, we need two key pieces of information: the number of favorable outcomes (i.e., the number of medium shirts) and the total number of possible outcomes (i.e., the total number of shirts).

This is where our shirt inventory table comes to the rescue. It provides us with all the information we need to calculate the probability. Remember, the table breaks down the shirts by color and size, giving us a clear picture of the inventory composition. To find the number of medium shirts, we need to look at the 'Medium' column. This column tells us the total number of medium shirts, regardless of color. So, before we jump into the calculation, let's recap the process. We're trying to find the probability of picking a medium shirt. This means we need to identify the number of medium shirts in the inventory and divide it by the total number of shirts. The table holds all the necessary information, and we're about to put it to work. So, let's dive into the next section and see how we can use the table to answer this question precisely.

Calculating the Probability

Now, for the moment of truth! Let's put our understanding of the table and probability to the test and calculate the probability of picking a medium shirt. As we discussed earlier, probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In our case, the favorable outcome is picking a medium shirt, and the total possible outcomes are the total number of shirts in the batch. To find the number of medium shirts, we turn to our trusty shirt inventory table. Remember the 'Medium' column? This is where we'll find the information we need. Looking at the table, we see that there are 48 medium red shirts and 40 medium blue shirts. To get the total number of medium shirts, we simply add these two numbers together:

48 (medium red shirts) + 40 (medium blue shirts) = 88 medium shirts

So, we have 88 medium shirts in our inventory. This is the numerator in our probability calculation. Next, we need the total number of shirts, which is given in the table as 165. This is our denominator. Now we have all the pieces of the puzzle! We can calculate the probability of picking a medium shirt by dividing the number of medium shirts by the total number of shirts:

Probability (picking a medium shirt) = Number of medium shirts / Total number of shirts

Probability (picking a medium shirt) = 88 / 165

To simplify this fraction, we can find the greatest common divisor (GCD) of 88 and 165, which is 11. Dividing both the numerator and the denominator by 11, we get:

Probability (picking a medium shirt) = (88 / 11) / (165 / 11)

Probability (picking a medium shirt) = 8 / 15

Therefore, the probability of picking a medium shirt at random from the batch of 165 shirts is 8/15. This fraction represents the likelihood of selecting a medium shirt, and it's a precise answer based on the data provided in the table. But what does this probability mean in practical terms? Let's explore the implications of this result in the next section.

Interpreting the Probability: What Does 8/15 Mean?

So, we've calculated that the probability of picking a medium shirt is 8/15. But what does this fraction actually tell us? How can we interpret this probability in a way that makes sense in the real world? Well, let's break it down. A probability of 8/15 means that if you were to randomly pick a shirt from the batch many, many times, you would expect to pick a medium shirt approximately 8 out of every 15 times. It's not a guarantee, of course. You might pick a medium shirt more or less than 8 times in 15 tries, especially if you only pick a few shirts. But over a large number of selections, the proportion of medium shirts picked would tend to approach 8/15.

To get a better feel for this probability, it can be helpful to convert it to a percentage. To do this, we simply divide 8 by 15 and multiply by 100:

(8 / 15) * 100 ≈ 53.33%

So, the probability of picking a medium shirt is approximately 53.33%. This means that there's a slightly higher than 50% chance of picking a medium shirt at random. In other words, medium shirts are slightly more prevalent in the inventory than non-medium shirts. This information could be valuable in various scenarios. For instance, if you're planning a promotional campaign and want to target a specific size, knowing the size distribution can help you make informed decisions. Or, if you're managing inventory and need to restock, this probability can guide your ordering strategy. The key takeaway here is that probability provides a quantitative way to express uncertainty. It allows us to make predictions and decisions based on data, rather than relying on guesswork. In this case, the probability of 8/15 (or 53.33%) gives us a clear understanding of the likelihood of picking a medium shirt, empowering us to make informed choices.

Conclusion: The Power of Data Analysis

Well, guys, we've reached the end of our journey into shirt statistics! We started with a seemingly simple table of data and, by understanding its structure and applying basic probability principles, we were able to answer a specific question: What is the probability of picking a medium shirt at random? We found that the probability is 8/15, or approximately 53.33%, meaning that medium shirts are slightly more prevalent in the inventory. But more importantly, we've demonstrated the power of data analysis. By organizing information in a clear and concise way, like in our shirt inventory table, we can extract valuable insights and make informed decisions. This skill is applicable in countless scenarios, from managing inventory in a clothing store to analyzing survey results or even understanding your own personal data.

The key takeaways from this exercise are twofold. First, understanding how to read and interpret data tables is crucial for anyone who wants to make sense of the world around them. Tables are a common way to present data, and knowing how to extract information from them is a valuable skill. Second, probability is a powerful tool for quantifying uncertainty and making predictions. By calculating probabilities, we can make informed decisions based on data, rather than relying on gut feelings or guesswork. So, the next time you encounter a table of data, don't be intimidated! Remember the steps we took today: understand the table's structure, identify the relevant information, and apply the appropriate principles (like probability) to answer your question. With a little practice, you'll become a data analysis pro in no time! And who knows, maybe you'll even use your newfound skills to optimize your own wardrobe! Thanks for joining me on this statistical adventure, and I hope you found it both informative and engaging.