Question

The Bookstall Inc. is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are $1.85 each, and hardcover books are $4.85. Of the 100 books sold last Tuesday morning, 85 were paperback and the rest were hardcover.

What was the weighted mean price of a book? (Round your answer to 2 decimal places.)

1. Weighted Mean $________

Answer 1

Since, as we know that Weighted mean.

Weighted mean is nothing but its is mean of sum of products of it's means and number of observations i.e.

$\bar_x$ = $\frac{N_p * W_p + N_h * W_h }{N_p + N_h}$

Here, $N_p$ = Number of paperback ,

$N_h$ = Number of hardcover,

$W_p$ = Mean of Cost of Paperback,

$W_h$ = Mean of Cost of hardcover.

Given, Total number of paperback = 85

and total number of hardcover books = 100 - 85 = 15

Cost of each paperback = $1.85

$\implies$Cost of 85 paperbacks = 85 * $1.85 = $157.25

Therefore ,Mean of cost of 85 paperbacks = $\frac{157.25}{85}$ = $1.85

Now, Cost of each hardcover = $4.85

$\implies$Cost of 15 hardcovers = 15 * $4.85 = $72.75

Therefore, Mean of cost of 15 hardcovers = $\frac{72.75}{15}$ = $4.85

$\implies$ Using formula for weighted mean = $\frac{85 * 1.85 + 15 * 4.85}{85 + 15}$

$\implies$ Weighted Mean = $\frac{157.25 + 72.75}{100}$ =  $\frac{230}{100}$ = $2.30$. (upto 2 decimal places)