The dot plot displays the number of marshmallows added to hot cocoa by several kids. What is the MAD (mean absolute deviation) of the data represented in the dot plot

A.0.6 marshmallows
B. 3 marshmallows
C.4 marshmallows
D. 5 marshmallows

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

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.

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.

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft