Foreword
"Please tell Kat that Brainly gives half the points she selects to each user that answers the question."
The Answers
#1:
We are trying to find the MAD for each set of the teachers' grades. To find the MAD (again) find the mean of the teachers' grades. Then, take each of the teachers' grades and find the absolute value of the difference between that grade and the mean grade. Add the differences up, and divide the result by the number of teachers (10).
Do the first table first (first things first!). Find the mean by adding up the grades and dividing them by the number of teachers (10).
76 + 81 + 85 + 79 + 89 + 86 + 84 + 80 + 88 + 79 = 827
827/10 = 82.7
The mean grade for the first table is 82.7.
Now, we need to find the absolute value of the difference between each of the teachers' grades and the mean.
82.7 - 76 = 6.7
82.7 - 81 = 1.7
85 - 82.7 = 2.3
82.7 - 79 = 3.7
89 - 82.7 = 6.3
86 - 82.7 = 3.3
84 - 82.7 = 1.3
82.7 - 80 = 2.7
88 - 82.7 = 5.3
82.7 - 79 = 3.7
Now, we need to add up the result.
6.7 + 1.7 + 2.3 + 3.7 + 6.3 + 3.3 + 1.3 + 2.7 + 5.3 + 3.7 = 37
Now, we divide the result by the number of teachers.
37/10 = 3.7
So the MAD for the first table is 3.7.
Now we do the same thing for the second table.
[tex]Mean= \frac{sum\ of\ grades}{10} [/tex]
79 + 82 + 84 + 81 + 77 + 85 + 82 + 80 + 78 + 83 = 811
811/10 = 81.1
Bad grades.
[tex]MAD= \frac{absolute\ value\ of\ difference\ of\ each\ grade\ from\ the\ mean}{10} [/tex]
81.1 - 79 = 2.1
82 - 81.1 = 0.9
84 - 81.1 = 2.9
81.1 - 81 = 0.1
81.1 - 77 = 4.1
85 - 81.1 = 3.9
82 - 81.1 = 0.9
81.1 - 80 = 1.1
81.1 - 78 = 3.1
83 - 81.1 = 1.9
Add.
2.1 + 0.9 + 2.9 + 0.1 + 4.1 + 3.9 + 0.9 + 1.1 + 3.1 + 1.9 = 21
21/10=2.1
Now, we compare the MAD's. If the MAD for the second table is greater than the MAD for the first table, then the teachers have not improved/were sleeping. If not, then the teachers have improved/got lucky.
[tex]MAD_{1st\ table}=3.7[/tex]
[tex]MAD_{2nd\ table}=2.1[/tex]
Hooray! They improved/got lucky, by 1.6 points to be precise.
#2:
Remember from the previous answer I gave (the other question you asked) the example with a MAD of 0? That's because they were all exactly on the mean (4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 40, 40/10 = 4, MAD = 0). Therefore, if the MAD of the teachers' grades was zero, that means they all got the same score! Hooray! Mission accomplished. Or the common core machine has succeeded in producing identical copies of teachers.
Backword
I hope you know what the MAD is now.
