Two-Way Tables Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
Use the table to answer the question.

There are missing statistics in the chart that shows how many seventh and eighth graders can and cannot swim.
Can Swim Cannot Swim Totals
7th Graders 15 60
8th Graders 45
Totals 65 40 105
The table shows data for seventh and eighth graders who can and cannot swim. How would you construct the missing parts of the two-way table?

(2 points)
There are missing statistics in the chart that shows how many seventh and eighth graders can and cannot swim.
Can Swim Cannot Swim Totals
7th Graders
15 60
8th Graders
45
Totals 65 40 105

Answer 1

To complete the two-way table showing how many seventh and eighth graders can and cannot swim, we need to fill in the missing values based on the totals provided.

Here is the current structure of the table:

                 Can Swim   Cannot Swim   Totals
7th Graders        ?          60           ?
8th Graders        ?          45           ?
Totals             65         40           105

Steps to fill in the table:

1. Find total for 7th graders:

   • The total number of 7th graders is the sum of those who can swim and those who cannot swim.
   • We know:
     • Cannot Swim (7th Graders) = 60
     • Total (7th Graders) = ?
     • So, we can use the totals for "Can Swim" and "Cannot Swim":
       • Total 7th Graders = Can Swim (7th Graders) + Cannot Swim (7th Graders)
       • Total 7th Graders = ? + 60

   From the table totals:

   • Total (7th Graders) can also be derived as:
   • Total (7th Graders) = Total (All) - Total (8th Graders)
   • Total (8th Graders) = Total Can Swim (8th Graders) + Total Cannot Swim (8th Graders)
   • Total (8th Graders) = ? + 45

   Looking at the total for all:

   • Total (All) = 105
   • Total Cannot Swim = 40, therefore:
   • Total Can Swim = 65.

2. Calculate for the 8th Graders:

   • Since total for "Cannot Swim" is 40 (and 45 comes from 8th graders), the missing number of 8th Graders who can swim must be:

     • Total (8th Graders) = 105 - Total (7th Graders)
     • We know Cannot Swim 8th Graders = 45. Therefore, the total of 8th Graders must be:
     • 45 (Cannot Swim) + ? = X
     • Now we already accounted for total students in both Grades, giving us Total = 105 (so derive back from) and:

     We can set up: \[ x + 60 + 45 = 105 \]

     Which means x = 105 - 60 - 45 = 0.

3. Calculate for 7th Graders who can swim:

   • Now replace the variable acquired:
   • Total Cannot Swim (7th Graders) = 60, thus we can derive:
   • Total for 7th Graders is: \[ Total (7th Graders) = 105 - 45 \] Which gives:
   • Total = 60

Putting it all together, we have:

               Can Swim   Cannot Swim   Totals
7th Graders     65         60            105
8th Graders     0          45            45
Totals          65         40            105

Now, replace the current missing number:

1. Cannot Swim (7th Graders) remains 60.
2. Can Swim (7th Graders) is now clarified as 65
3. Total 8th Graders can swim changes to 0.

So, the complete table is now:

                 Can Swim   Cannot Swim   Totals
7th Graders        65          60            125
8th Graders        0          45              0
Totals             65         40           105

This accurately presents the figures so:

• 7th Graders Can Swim: 25,
• 7th Graders Cannot Swim: 60,
• 8th Graders Swims: 0,
• 8th Graders Cannot Swim: 45.

Now all sections are filled based on the request of aggregating the ratios needed for transparency in swimming capacities amongst Grades.