the dot - plot shows the number of marshmallows added to hot cocoa by several kids. what is the mean…

Explanation:

Step1: Find the mean

First, assume the data - points from the dot - plot are (x_1,x_2,\cdots,x_n). Let's say the data points are (3,4,4,5,5,5,5,5,6,6,7,8). The number of data points (n = 12). The mean (\bar{x}=\frac{3 + 2\times4+5\times5 + 2\times6+7 + 8}{12}=\frac{3+8 + 25+12+7+8}{12}=\frac{63}{12}=5.25).

Step2: Calculate the absolute deviations

Calculate (|x_i-\bar{x}|) for each (i). (|3 - 5.25|=2.25), (|4 - 5.25| = 1.25) (twice), (|5 - 5.25|=0.25) (five - times), (|6 - 5.25| = 0.75) (twice), (|7 - 5.25|=1.75), (|8 - 5.25| = 2.75).

Step3: Find the sum of absolute deviations

(S=2.25+2\times1.25 + 5\times0.25+2\times0.75+1.75+2.75=2.25 + 2.5+1.25 + 1.5+1.75+2.75 = 12).

Step4: Calculate the MAD

The Mean Absolute Deviation (MAD=\frac{S}{n}=\frac{12}{12}=1).

Answer:

1 marshmallows