Question

The mean grades of 30 students in both math and science is 85. If the mean absolute deviation of the grades in math is 1 and the mean absolute deviation for the grades in science is 8, which of the following statements is true?
A. The students scored higher grades in math than in science.
B. The grades of the students in science are a lot closer to 85 than the grades of the students in math.
C. The grades of the students in math are a lot closer to 85 than the grades of the students in science.
D. The students scored lower grades in math than in science.

Answer 1

Answer:

Options C is correct

Step-by-step explanation:

Given that The mean grades of 30 students in both math and science is 85

But mean absolute deviation i.e. the sum of absolute values of deviations for Math is 1 but for Science is 8.

This implies that

C) The grades of the students in math are a lot closer to 85 than the grades of the students in science.

Option A cannot be right because only absolute deviation is more hence can be either lower or higher.

On the same grounds Option D is also wrong.

Option B is wrong because Science has more absolute mean deviation

Only option C is right.

Answer 2

Mean is the same thing as average
example
the mean of 30 and 40 is 35 because (30+40)/2=70/2=35

mean absolue deviation is when you take the mean of the set
then you find the diffference of each number of the set then take the mean of that
ex if yo uhave 1,2,3,4,5 and the mean is 3, then ou find the absolute value of the difference of each
|1-3|=2
|2-3|=1
|3-3|=0
|4-3|=1
|5-3|=2
add them and divide by 5
(2+1+0+1+2)/5=6/5= MAD=6/5

basically it tells how spread out the graph is or how close the points are to the mean
so the smaller mean average deviation, the closer the points are to the mean
the bigger it is, the farther they are

so if they had the points 1,2,3,4,5 and mean is 3 and MAD=6/5, 6/5 is small so therefor the points are close to that number
if I had the points 1,1,1,2,5,5 and the mean was 3 and MAD=11/5, 11/5 is bigger than 6/5 and therefor the points are more spread out


therefor the math scores are closer togeher
science is farther apart

if you mean that the highest grade in math was compared witht eh highest grade in science, then science is higher since the plots are more spread out

since math had a smaller MAD than science, the points are closer together

so the answers are C and D