answer:A weighted average, also known as a weighted mean, is a type of average that takes into account the relative importance or weights of the individual values being averaged. This is different from a simple average, also known as an arithmetic mean, which gives equal weight to each value. To calculate a weighted average, each value is multiplied by its corresponding weight, and then these products are added together. The sum is then divided by the total weight to get the weighted average. The weights can be based on various factors, such as the size of a group, the importance of a metric, or the frequency of an event. Compared to other types of averages, the weighted average is useful when: - The values being averaged have different levels of importance or influence. - The sizes of the groups being averaged vary significantly. - The data is hierarchical or has a complex structure. In contrast, a simple average is more suitable when all the values have equal importance or the data is relatively uniform. Other types of averages include: - Median: The middle value of a dataset when it is sorted in order. - Mode: The most frequently occurring value in a dataset. - Geometric mean: The nth root of the product of n values, used for averages of rates, ratios, or growth rates. - Harmonic mean: The reciprocal of the average of the reciprocals of the values, used for averages of rates, such as speeds or rates of return. The choice of average depends on the specific context and the characteristics of the data being analyzed. The weighted average is a powerful tool when working with complex or hierarchical data, as it allows for the incorporation of additional information to create a more nuanced and accurate average.

answer:Calculating a weighted average when the weights don't add up to 100, or more specifically, when the weights don't sum to 1, requires a simple adjustment. The goal is to normalize the weights so that they add up to 1, ensuring that the weighted average is calculated correctly. Here's the step-by-step process: 1. Calculate the sum of the weights: Add up all the weights to find the total weight. 2. Normalize the weights: Divide each weight by the total weight calculated in step 1. This will create new weights that add up to 1. 3. Calculate the weighted average: Multiply each value by its corresponding normalized weight and sum the results. 4. Divide by the sum of the normalized weights: Since the normalized weights already add up to 1, this step is technically not necessary. However, it's often included for clarity, as the weighted average is essentially the sum of the weighted values divided by the sum of the weights. Mathematically, if you have values x1, x2, ..., xn and weights w1, w2, ..., wn, the weighted average is calculated as: Weighted Average = (x1 * (w1 / Σwi)) + (x2 * (w2 / Σwi)) + ... + (xn * (wn / Σwi)) where Σwi is the sum of all the weights. Alternatively, you can simplify the calculation by dividing the sum of the weighted values by the sum of the weights: Weighted Average = (x1 * w1 + x2 * w2 + ... + xn * wn) / Σwi Both methods will give you the correct weighted average, even when the original weights don't add up to 100 or 1.

answer:Weighted averages are indeed more commonly encountered in real-world applications, such as finance, economics, and business, rather than in basic school work. However, understanding weighted averages can be beneficial in various areas, including: 1. **Cost accounting**: As you mentioned, weighted averages are used to calculate the average cost of goods or services, taking into account the varying costs and quantities of different components or materials. 2. **Stock values**: Weighted averages are used to calculate the average stock price, considering the number of shares traded at each price point. 3. **Portfolio analysis**: Weighted averages help investors calculate the overall return on investment (ROI) of a portfolio, taking into account the different weights of individual assets. 4. **Survey research**: Weighted averages can be used to analyze survey data, where different respondents or groups may have varying levels of influence or representation. 5. **Grade calculation**: Some educational institutions use weighted averages to calculate student grades, where different assignments or exams have varying weights or importance. 6. **Supply chain management**: Weighted averages can help analyze and optimize supply chain operations, considering factors like transportation costs, inventory levels, and demand forecasts. 7. **Economic indicators**: Weighted averages are used to calculate economic indicators, such as the Consumer Price Index (CPI), which measures inflation by weighting the prices of different goods and services. These real-world applications highlight the importance of understanding weighted averages, even if they may not be as prominent in basic school work. As students progress to more advanced studies or enter the workforce, they will likely encounter weighted averages in various contexts.

answer:Let the two numbers be x and y, where x>y. We are given that x+y=30 and x-y=4. Adding these two equations, we get 2x=34, so x=17. Therefore, the larger of the two numbers is boxed{17}. The answer is: 17