Problem 14 - Basic Statistics for Business and Economics with Student

Question

The Bookstall, Inc., is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are \(\$ 1.00\) each, and hardcover books are \(\$ 3.50 .\) Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

Step-by-Step Solution

Answer

The weighted mean price of a book is $1.50.

Step 1: Identify the Quantities Sold

Out of 50 books sold, 40 were paperback, and the rest were hardcover. This means 10 books were hardcover since we subtract the number of paperbacks from the total books sold: \( 50 - 40 = 10 \).

Step 2: Determine the Prices of Each Book Type

Paperback books are priced at \( \\(1.00 \) each, and hardcover books are \( \\)3.50 \) each.

Step 3: Calculate Total Cost for Each Book Type

The total cost for paperback books is \( 40 \times 1.00 = \\(40.00 \).The total cost for hardcover books is \( 10 \times 3.50 = \\)35.00 \).

Step 4: Calculate Overall Total Cost

Add the total cost from each type: \( 40 + 35 = \$75.00 \).

Step 5: Calculate the Weighted Mean

The weighted mean price per book is the total cost divided by the total number of books: \( \frac{75}{50} = \$1.50 \).

Key Concepts

Statistics

When dealing with data like book pricing at a bookstore, statistics help us summarize and interpret the data effectively. One important statistical measure in this scenario is the weighted mean. Weighted mean helps combine elements of data that have different significance or weights. In our example, different types of books (paperbacks and hardcovers) have different prices.

Understanding weighted mean is crucial here as it provides a more accurate average that accounts for the varying numbers of each type of book sold. Unlike a simple average, the weighted mean reflects the actual distribution and importance of each data point, making it particularly useful in cases like this where each group of data contributes differently to the overall average.

• The weighted mean considers the frequency of items (number of books sold).
• It incorporates the cost of each item type (price of paperbacks vs. hardcovers).

Quantitative Analysis

Quantitative analysis involves using mathematical and statistical models to analyze measurements and come to conclusions. It is a powerful tool in understanding and interpreting data sets, such as the sales of various book types with different prices.

In the scenario described, we performed a quantitative analysis by calculating total sales and the overall sales average (weighted mean). This approach allowed us to derive meaningful insights from selling paperback and hardcover books with distinct pricing structures.

• First, we identify the quantity of each book type sold.
• Next, we calculate the total revenue generated by each type.
• The aim is to assess various economic indicators, such as total cost and average pricing, which in this case, is the weighted mean.

This type of analysis helps booksellers like The Bookstall, Inc. understand not just how many books are sold, but how the pricing of each type contributes to their overall earnings.

Book Pricing

Understanding book pricing is essential in running a bookstore, especially when offering diverse types of books, such as paperbacks and hardcovers, that are priced differently. Different pricing strategies can impact sales volume and revenue.

In The Bookstall, Inc. exercise, paperback books are priced at $1.00, whereas hardcover books are $3.50 each. These differing prices mean that even if fewer hardcovers are sold, they contribute more significantly to revenue than paperbacks do. Such a pricing strategy needs to be closely monitored to ensure that it aligns with sales goals and customer demand.

• Paperback books are affordable and may sell in higher volumes.
• Hardcovers, being more expensive, might sell less but contribute substantially to revenues per sale.

Therefore, understanding book pricing and the impact on overall sales via techniques like weighted mean can guide effective business strategies and optimize sales performance.