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Statistics is the field that involves collecting, analyzing, interpreting, and presenting data. One key concept in statistics is the weighted mean, a type of average that takes into account the importance or "weight" of different values. Unlike a simple mean which treats each data point equally, a weighted mean assigns a specific importance to each. This makes it especially useful in scenarios where some data points have more significance, like in this bookstore example with different prices for paperbacks and hardcover books. The formula for the weighted mean is the sum of each value multiplied by its weight, divided by the sum of all weights. In essence, it gives us an average that mirrors reality more closely when values have different levels of importance.

Problem-solving in mathematics involves a methodical approach to break down complex problems into manageable steps. In this exercise, identifying the key components was crucial. First, we distinguished the two categories of books: paperbacks and hardcovers. Each of these had specific counts and prices, which formed the basis of our weights and values.

• Determine the important factors, such as the number of each type of book and their prices.
• Understand how these factors interplay to form the desired outcome, which in this case, is the weighted mean price.

By organizing these components clearly, the problem becomes less intimidating and more solvable. Clear identification and organization of data lead to a logical and straightforward solution.

Mathematics calculations often follow straightforward yet vital steps. Breaking down the math problem in this exercise involves simple multiplication and division. First, we multiply the number of paperbacks by their price to get the total spent on paperbacks, which is simple arithmetic: 40 paperbacks times \(1.00 equals \)40.00.
Likewise, for hardcovers: 10 times \(3.50 yields \)35.00.Next, these total costs are added together to get the overall cost of the books sold, $75.00 in this case. The final step is dividing this total cost by the total number of books (50). This gives us the weighted mean:\[ \frac{75.00}{50} = 1.50 \]These steps highlight the importance of orderly calculations in solving math problems efficiently. Even in straightforward arithmetic, clear steps contribute significantly to accurate and straightforward solutions.