We know that 70 sixth graders had an average weight of 90 pounds, and 30 seventh graders had an average weight of 100 pounds.
We know that the weight of all 70 sixth graders will be 70*90, since we're multiplying the total amount of students by the average.
Using this same logic tells us that the total weight for the 30 seventh graders is 30*100
The average weight for all 100 students will be the total weight of the sixth graders (which is 70*90) added with the total weight of the seventh graders (which is 30*100), then finally divided by the total amount of students in the sample space (which is 100).
[tex]\dfrac{70(90)+30(100)}{100}[/tex]
[tex]=\dfrac{6300+3000}{100}[/tex]
[tex]=\dfrac{9300}{100}[/tex]
[tex]=93[/tex]
The average of all 100 students is 93 pounds.
Let me know if you need any clarifications, thanks!
