/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 The Bookstall, Inc., is a specia... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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?

Short Answer

Expert verified
The weighted mean price of a book is $1.50.

Step by step solution

01

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: \( 50 - 40 = 10 \).
02

Determine the Prices of Each Book Type

Paperback books are priced at \( \\(1.00 \) each, and hardcover books are \( \\)3.50 \) each.
03

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 \( 10 \times 3.50 = \\)35.00 \).
04

Calculate Overall Total Cost

Add the total cost from each type: \( 40 + 35 = \$75.00 \).
05

Calculate the Weighted Mean

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The State of Indiana and the Kelley School of Business of Indiana University offer links to many data sources. Go to www.stats.indiana.edu, then, under the heading Social and Economic indicators select Birth/Marriage/Death, under state comparisons, select Annual Vital Statistics Data, for Geography Type choose U.S. and 50 States, for Specific Geography select all states, and finally select Get Data. The information can be output in Excel format. Suppose you are interested in the typical number of births per state. Compute the mean, median, and the standard deviation of the number of births per state and the number of births per 1000 population by state for the latest year available. You should be able to download this information into a software package to perform the calculations. Which of the measures of location is the most representative? Which data set would you recommend using: number of births per state or the number of births per 1000 population? Why? Suppose you are interested in birth rates for the 50 states and Washington, D.C. Compute the mean, median, and standard deviation. Write a brief report summarizing the data.

46\. The annual incomes of the five vice presidents of TMV Industries are: \(\$ 125,000 ; \quad \$ 128,000 ; \quad \$ 122,000 ;\) \(\$ 133,000 ;\) and \(\$ 140,000 .\) Consider this a population. a. What is the range? b. What is the arithmetic mean income? c. What is the population variance? The standard deviation? d. The annual incomes of officers of another firm similar to TMV Industries were also studied. The mean was \(\$ 129,000\) and the standard deviation \(\$ 8,612 .\) Compare the means and dispersions in the two firms.

A southern state has seven state universities in its system. The numbers of volumes (in thousands) held in its libraries are \(83,510,33,256,401,47,\) and \(23 .\) a. Is this a sample or a population? b. Compute the standard deviation.

Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23,19,26,17,21,24,22 a. Compute the mean number and median number of apples in a bag. b. Verify that \(\Sigma(x-\bar{x})=0\)

There were five customer service representatives on duty at the Electronic Super Store during last weekend's sale. The numbers of HDTVs these representatives sold are: \(5,8,4,10,\) and 3

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.