Question

The line plot shows that you packed 10 boxes of different weights

Answer 1

The dot plot shows that 10 boxes were packed with different weights of books.

You have to determine how to repack the boxes so that each one has the same weight.

The first step is to determine the total weight of books you have to pack.

Looking at the dot plot, each x-mark indicates one box so that:

1 box has a weight of 1/8 pounds

3 boxes have a weight of 3/8 pounds

4 boxes have a weight of 4/8 pounds

2 boxes have a weight of 7/8 pounds

To calculate the total weight, you have to multiply each weight by the number of boxes that measure it and add all results, i.e. multiply each obervation (weight) by the observed frequency (number of boxes):

`\begin{gathered} \text{Total weight=observed wight }\cdot\text{ nºboxes} \\ \text{Total weight=(1}\cdot(1)/(8)\text{)+(3}\cdot(3)/(8)\text{)+(4}\cdot(4)/(8)\text{)+(2}\cdot(7)/(8)\text{)} \\ \text{Total weight=5} \end{gathered}`

All the books that were packed inside the 10 boxes add up to a total weight of 5 pounds.

Now that we know the total weight, to distribute it evenly in the 10 boxes you have to divide the total weight by the number of boxes:

`\frac{\text{total weight}}{nºboxes}=(5)/(10)=(1)/(2)`

To repack the boxes evenly, you have to pack 1/2 pound of books in each box. (2nd option)