Respuesta :
Answer:
The mean absolute deviation (MAD) of the dataset is 33.333.
Step-by-step explanation:
The mean absolute deviation (MAD) of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
These are the steps to calculate the mean absolute deviation.
Step 1: Calculate the mean.
[tex]Mean = \frac{20+90+25+100+85+30}{6} =\frac{175}{3}\approx58.333[/tex]
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
[tex]|20-\frac{175}{3} |=\frac{115}{3}\\\\|90-\frac{175}{3} |=\frac{95}{3}\\\\|25-\frac{175}{3} |=\frac{100}{3}\\\\|100-\frac{175}{3} |=\frac{125}{3}\\\\|85-\frac{175}{3} |=\frac{80}{3}\\\\|30-\frac{175}{3} |=\frac{85}{3}[/tex]
Step 3: Add those deviations together.
[tex]\frac{115}{3}+\frac{95}{3}+\frac{100}{3}+\frac{125}{3}+\frac{80}{3}+\frac{85}{3}=\frac{600}{3}=200[/tex]
Step 4: Divide the sum by the number of data points.
[tex]MAD=\frac{200}{6} =33.333[/tex]
