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

The difference of weight is
`2` pounds.

Explanation:

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

To find: 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.

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

`1(1)/(2) lb=(2+1)/(2)=(3)/(2)lb`

`1(1)/(4) lb=(4+1)/(4)=(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
`(3)/(2) lb` and how many grapefruit we have of weight
`(5)/(4) lb`. In other words, we need to know, in the diagram, how many points there are about class of
`(3)/(2) lb` and how many points there are about class of
`(5)/(4) lb`.

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

`x (1(1)/(2) ) - y (1(1)/(4) ) = Z`

Where

`Z`: Weight difference

`x`: Quantity of
`1(1)/(2) lb` grapefruit

`y`: Quantity of
`1(1)/(4)lb` grapefruit

Suppose that of the
`10` total grapefruits,
`3` of them weigh
`1(1)/(2) lb` and
`2` of them weigh
`1 (1)/(4)` pounds. This is:
`x=3` and
`y=2`

Now,

`3((3)/(2) )-2((5)/(4) )`

`=(9)/(2) -(5)/(2)`

`=(4)/(2)`

`=2`

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