Answer: 0.6 marshmallows (choice A)
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Step-by-step explanation:
The dot plot is of these values
3, 4, 5, 5, 5, 5, 5, 5, 6, 7
The unique values are 3,4,5,6,7 where the '5' shows up six times while the other values only show up exactly one time.
Adding up those values gets us
3 + 4 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 7 = 50
Then we divide by 10 because there are 10 items in the original list. So that leads to the arithmetic mean 50/10 = 5
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The next step is to subtract the mean from each data value
We'll apply absolute value to ensure the results are never negative. So this is where the "absolute" comes from in "mean absolute deviation". The "deviation" portion is another way of saying distance. Specifically, we're looking for the distance from the mean.
- |3-mean| = |3-5| = |-2| = 2
- |4-mean| = |4-5| = |-1| = 1
- |5-mean| = |5-5| = |0| = 0
- |5-mean| = |5-5| = |0| = 0
- |5-mean| = |5-5| = |0| = 0
- |5-mean| = |5-5| = |0| = 0
- |5-mean| = |5-5| = |0| = 0
- |5-mean| = |5-5| = |0| = 0
- |6-mean| = |6-5| = |1| = 1
- |7-mean| = |7-5| = |2| = 2
We then have the new set {2,1,0,0,0,0,0,0,1,2} where there are 6 copies of "0" in the middle. We also have two copies of "1" and "2" each.
Let's find the arithmetic mean of this new set
Add the values: 2+1+0+0+0+0+0+0+1+2 = 6
Divide by 10 to get: 6/10 = 0.6 which is the final answer
This represents the average absolute value distance each value is from the mean.