Question

the dot plot displays the number of marshmallows added to hot cocoa by several kids. what is the mad of the data represented in the dot plot? a 0.6 marshmallows b 3 marshmallows c 4 marshmallows d 5 marshmallows

Explanation:

Step1: Find the mean

First, count the number of data - points. There is 1 point at 3, 1 at 4, 6 at 5, 1 at 6, 1 at 7. The total number of data - points $n=1 + 1+6 + 1+1=10$.
The sum of the data is $3\times1 + 4\times1+5\times6 + 6\times1+7\times1=3 + 4+30 + 6+7 = 50$.
The mean $\bar{x}=\frac{50}{10}=5$.

Step2: Calculate the absolute deviations

For $x_1 = 3$, the absolute deviation $\vert x_1-\bar{x}\vert=\vert3 - 5\vert = 2$.
For $x_2 = 4$, the absolute deviation $\vert x_2-\bar{x}\vert=\vert4 - 5\vert = 1$.
For the 6 data - points of $x = 5$, the absolute deviation $\vert x-\bar{x}\vert=\vert5 - 5\vert = 0$ (and the sum of these 6 absolute - deviations is $0\times6 = 0$).
For $x_3 = 6$, the absolute deviation $\vert x_3-\bar{x}\vert=\vert6 - 5\vert = 1$.
For $x_4 = 7$, the absolute deviation $\vert x_4-\bar{x}\vert=\vert7 - 5\vert = 2$.
The sum of the absolute deviations is $2\times1+1\times1 + 0\times6+1\times1+2\times1=2 + 1+0 + 1+2 = 6$.

Step3: Calculate the MAD

The mean absolute deviation (MAD) is $\frac{\text{Sum of absolute deviations}}{n}$.
So, $MAD=\frac{6}{10}=0.6$.

Answer:

A. 0.6 marshmallows