Question

The line plots shows the weights of 9 grapefruits. What is the difference in the total weight of all the 1 1/2 lb grapefruits and the total weight of all the 1 1/4 lb grapefruits? A 1/4lb B 2 lb C 4 1/2lb D 7 lb

Answer 1

Answer:

The difference of weight is $2$ pounds.

Step-by-step explanation:

Given:  The line plots shows the weights of $9$ grapefruits

To find: The difference in the total weight of all the $1\frac{1}{2} lb$  grapefruits and the total weight of all the $1 \frac{1}{4}lb$ grapefruits.  

Firstly, we need to convert the given mixed fractions as following:

$1\frac{1}{2} lb=\frac{2+1}{2}=\frac{3}{2}lb$

$1\frac{1}{4} lb=\frac{4+1}{4}=\frac{5}{4}lb$

Now, we know that,

Point diagrams divide a sample into different classes, and allow to observe the frequencies of each class.

In this case, the different weights of the grapefruit constitute the classes. From a sample of 10 grapefruit, some will weigh  others weigh.

We need to observe the dot diagram to know how many  grapefruit we have of weight $\frac{3}{2} lb$ and how many  grapefruit we have of weight $\frac{5}{4} lb$. In other words, we need to know, in the diagram, how many points there are about class of  $\frac{3}{2} lb$ and how many points there are about class of   $\frac{5}{4} lb$.

Then, the total difference between all grapefruit of  pounds and all grapefruit of pounds is calculated as follows:

$x (1\frac{1}{2} ) - y (1\frac{1}{4} ) = Z$

Where

$Z$: Weight difference

$x$: Quantity of $1\frac{1}{2} lb$  grapefruit

$y$: Quantity of $1\frac{1}{4}lb$ grapefruit

Suppose that of the $10$ total grapefruits, $3$ of them weigh $1\frac{1}{2} lb$  and $2$ of them weigh $1 \frac{1}{4}$  pounds. This is: $x=3$ and $y=2$

Now,

$3(\frac{3}{2} )-2(\frac{5}{4} )$              

$=\frac{9}{2} -\frac{5}{2}$                    

$=\frac{4}{2}$            

$=2$

Hence, for this case, the difference of weight is $2$ pounds.