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What is the mean absolute deviation (MAD) of the data set? Round your answer to the nearest tenth, if necessary. {9.1, 9.3, 9.1, 9.5, 9.8, 9.9}

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Hello there, and thank you for posting your question here on brainly.

Ok, to find MAD, you have to add up all of the decimals in the set, and then divide by how much decimals there are in the set.

Adding them all up...

The final result of the adding is 56.7

Now, we have to divide by how much decimals.

We now have. 56.7 / 6

Do the division.

56.7 / 6 ===> 9.45

No need to round, the final answer is 9.4

Hope this helped!! ☺♥

Answer:

The mean absolute deviation of the data set is [tex]MAD \approx 0.3[/tex]

Step-by-step explanation:

The mean absolute deviation 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.

To find the mean absolute deviation you must:

1. Calculate the mean

Found by adding all data points and dividing by the number of data points.

[tex]\mu=\frac{9.1+9.3+9.1+9.5+9.8+9.9}{6} \\\\\mu = \frac{56.7}{6}\\\\\mu=9.45[/tex]

2. Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

[tex]\begin{array}{cc}Data \:point&Distance \:from \:mean\\9.1&|9.1-9.45|=0.35\\9.3&|9.3-9.45|=0.15\\9.1&|9.1-9.45|=0.35\\9.5&|9.5-9.45|=0.05\\9.8&|9.8-9.45|=0.35\\9.9&|9.9-9.45|=0.45\end{array}[/tex]

3. Add those deviations together.

[tex]0.35+0.15+0.35+0.05+0.35+0.45=1.7[/tex]

4. Divide the sum by the number of data points.

[tex]MAD=\frac{1.7}{6} \approx 0.28333\approx 0.3[/tex]

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