there were 6 rain - storms last summer. the amount of rainfall during each storm was 6 centimeters 3…

there were 6 rain - storms last summer. the amount of rainfall during each storm was 6 centimeters 3 centimeters 1 centimeter 8 centimeters 7 centimeters 9 centimeters. what was the mean absolute deviation of the rainfall amounts? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): centimeters

there were 6 rain - storms last summer. the amount of rainfall during each storm was 6 centimeters 3 centimeters 1 centimeter 8 centimeters 7 centimeters 9 centimeters. what was the mean absolute deviation of the rainfall amounts? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): centimeters

Answer

Explanation:

Step1: Calculate the mean

Let the rainfall amounts be (x_1 = 6), (x_2=3), (x_3 = 1), (x_4=8), (x_5=7), (x_6 = 9). The mean (\bar{x}=\frac{6 + 3+1+8+7+9}{6}=\frac{34}{6}=\frac{17}{3}\approx5.67)

Step2: Calculate the absolute - deviations

(\vert x_1-\bar{x}\vert=\vert6 - \frac{17}{3}\vert=\vert\frac{18 - 17}{3}\vert=\frac{1}{3}\approx0.33) (\vert x_2-\bar{x}\vert=\vert3-\frac{17}{3}\vert=\vert\frac{9 - 17}{3}\vert=\frac{8}{3}\approx2.67) (\vert x_3-\bar{x}\vert=\vert1-\frac{17}{3}\vert=\vert\frac{3 - 17}{3}\vert=\frac{14}{3}\approx4.67) (\vert x_4-\bar{x}\vert=\vert8-\frac{17}{3}\vert=\vert\frac{24 - 17}{3}\vert=\frac{7}{3}\approx2.33) (\vert x_5-\bar{x}\vert=\vert7-\frac{17}{3}\vert=\vert\frac{21 - 17}{3}\vert=\frac{4}{3}\approx1.33) (\vert x_6-\bar{x}\vert=\vert9-\frac{17}{3}\vert=\vert\frac{27 - 17}{3}\vert=\frac{10}{3}\approx3.33)

Step3: Calculate the mean absolute deviation

(MAD=\frac{\frac{1}{3}+\frac{8}{3}+\frac{14}{3}+\frac{7}{3}+\frac{4}{3}+\frac{10}{3}}{6}=\frac{\frac{1 + 8+14+7+4+10}{3}}{6}=\frac{\frac{44}{3}}{6}=\frac{44}{18}=\frac{22}{9}\approx2.4)

Answer:

(2.4)