Employee Wage Calculation In Textile Company: Frequency Table Analysis

Hey guys, ever wondered how companies figure out the average wages of their employees? Well, let's dive into a real-world example using a frequency table from a textile company. This table breaks down employee wages into classes, showing how many employees fall into each wage range. We're going to break down how to interpret this table and understand the distribution of wages within the company. So, let's get started and make sense of these numbers!

Understanding the Frequency Table

First off, let's break down the frequency table we're dealing with. The table shows the weekly wages of some textile company employees, measured in thousands of rupiah. It's divided into two main columns: Class and Frequency. The Class column represents wage ranges (like 150 - 179 thousand rupiah), and the Frequency column tells us how many employees fall into each of those ranges. For instance, if the table shows a frequency of 12 for the class 150 - 179, that means 12 employees earn wages within that range. This kind of data organization is super useful for getting a quick snapshot of how wages are distributed across the workforce. We can see where the majority of employees' earnings lie and identify any significant clusters or gaps in the wage structure. Understanding this distribution is the first step in analyzing the overall compensation structure within the company. We'll use these numbers to calculate different statistical measures, giving us a clearer picture of the average wage and how wages are spread out.

Analyzing the Data

Now, let's get our hands dirty with the data! To really understand what's going on with these wages, we need to calculate a few key things. First up, we can figure out the midpoint of each class. This is just the average of the lower and upper limits of each wage range. For example, for the class 150 - 179, the midpoint would be (150 + 179) / 2 = 164.5. These midpoints will help us estimate the average wage for each class. Next, we can calculate the weighted average wage. This is where we multiply each class midpoint by its frequency, add up all those results, and then divide by the total number of employees. This gives us a much more accurate picture of the average wage than simply adding up the class ranges and dividing. For instance, if we have a class with a midpoint of 200 and a frequency of 20, we multiply 200 by 20. We do this for every class, sum the results, and then divide by the total number of employees. This method accounts for the fact that some wage ranges have more employees than others, giving those ranges more weight in the final average. By calculating these statistics, we can start to see the central tendencies and distribution patterns in the employee wages. This is crucial for making informed decisions and understanding the overall financial health of the company.

Calculating the Mean (Average) Wage

Okay, let's crunch some numbers and find the mean, or average, wage. This is a crucial step in understanding the central tendency of the data. To calculate the mean, we need to find the midpoint of each class, as we discussed earlier, and then multiply each midpoint by its corresponding frequency. After that, we sum up all these products and divide by the total number of employees. Let's break it down step by step. First, calculate the midpoints: For the class 150 - 179, the midpoint is (150 + 179) / 2 = 164.5. For the class 180 - 209, the midpoint is (180 + 209) / 2 = 194.5. For the class 210 - 239, the midpoint is (210 + 239) / 2 = 224.5. Now, we multiply each midpoint by its frequency: 164.5 * 12 = 1974. 194.5 * 14 = 2723. 224.5 * 30 = 6735. Next, we sum up these products: 1974 + 2723 + 6735 = 11432. Finally, we divide by the total number of employees (12 + 14 + 30 = 56): 11432 / 56 ≈ 204.14. So, the mean wage is approximately 204.14 thousand rupiah. This tells us the average weekly wage of an employee in this company. It's a useful benchmark, but it's important to remember that the mean is just one piece of the puzzle. To get a complete picture, we also need to consider other measures, like the median and the mode, which can help us understand the distribution of wages and identify any potential outliers or skews in the data. Understanding the mean is a fundamental step, and now we can move on to more detailed analyses to gain even deeper insights.

Determining the Modal Class

Alright, let's switch gears and figure out the modal class. The modal class is simply the class with the highest frequency – the one that appears most often in our data set. In other words, it's the wage range where the most employees fall. Looking at our frequency table, we can quickly spot the class with the highest frequency. In this case, it's the class 210 - 239, with a frequency of 30. This means that more employees earn wages in the range of 210 to 239 thousand rupiah per week than in any other wage range. Identifying the modal class gives us a quick and easy way to understand the most common wage range within the company. It’s a valuable piece of information because it highlights where the majority of employees' earnings are clustered. This can be particularly useful for comparing the company's wage structure to industry benchmarks or for understanding how wages are distributed across the workforce. While the mean gives us the average wage, the modal class tells us what's typical. Together, these measures provide a more complete picture of the company's wage distribution. So, we've pinpointed the modal class, and now we can use this information to further analyze and interpret the wage data.

Estimating the Median Wage

Now, let's tackle the median wage. The median is the middle value in a dataset when the values are arranged in ascending order. It's another crucial measure of central tendency, and it's particularly useful because it's less sensitive to outliers than the mean. To estimate the median from a frequency table, we first need to find the median class. The median class is the class that contains the median value. To find it, we look for the class where the cumulative frequency is greater than or equal to half of the total frequency. Let's break it down. First, we calculate the total number of employees, which we already know is 56. Half of that is 56 / 2 = 28. Next, we need to calculate the cumulative frequencies: For the class 150 - 179, the cumulative frequency is 12. For the class 180 - 209, the cumulative frequency is 12 + 14 = 26. For the class 210 - 239, the cumulative frequency is 26 + 30 = 56. Now we look for the class where the cumulative frequency is greater than or equal to 28. In this case, it's the class 210 - 239, because its cumulative frequency (56) is the first one that exceeds 28. So, the median class is 210 - 239. To estimate the actual median wage within this class, we can use a formula that interpolates within the class boundaries. However, for simplicity, we can often use the midpoint of the median class as an estimate. The midpoint of the 210 - 239 class is (210 + 239) / 2 = 224.5. Therefore, we can estimate the median wage to be approximately 224.5 thousand rupiah. This means that about half of the employees earn less than 224.5 thousand rupiah, and about half earn more. Comparing the median to the mean can give us insights into the distribution's skewness. If the median is significantly different from the mean, it might indicate that the wage distribution is skewed, either towards higher or lower wages. By estimating the median, we gain another valuable perspective on the company's wage structure, complementing the mean and modal class.

Drawing Conclusions and Insights

Okay, we've crunched the numbers and found the mean, modal class, and estimated median wage. Now, let's put on our thinking caps and draw some conclusions. What does all this data tell us about the wages of employees at this textile company? First off, the mean wage we calculated was approximately 204.14 thousand rupiah. This gives us a general idea of the average weekly wage. The modal class, which is the wage range where the most employees fall, is 210 - 239 thousand rupiah. This indicates that a significant portion of the workforce earns within this range. We also estimated the median wage to be around 224.5 thousand rupiah. Because the median is higher than the mean, this suggests that the wage distribution might be slightly skewed towards lower wages. In other words, there might be some employees earning significantly lower wages that are pulling the average down. To get a fuller picture, we might want to look at the range of wages and how they're distributed across the different classes. Are there any significant gaps? Are there any outliers earning much more or much less than the majority? We could also compare this data to industry averages to see how this company's wages stack up against its competitors. Furthermore, analyzing the wage data over time could reveal trends and changes in the company's compensation practices. Are wages increasing, decreasing, or staying relatively stable? These are all valuable insights that can help the company make informed decisions about employee compensation and ensure fair and competitive wages. So, we've gone from raw data to meaningful insights, and that's the power of statistical analysis!

By analyzing the frequency table, we've gained a solid understanding of the wage distribution within the textile company. We've calculated key measures like the mean, modal class, and median, which provide valuable insights into the financial well-being of the employees. This kind of analysis is crucial for companies to make informed decisions about compensation and ensure a fair and competitive wage structure. Remember, data analysis is like detective work – each piece of information helps you solve the puzzle and understand the bigger picture. Keep exploring and stay curious, guys! You've got this!