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Determine the mean absolute deviation of the data.9, 7, 11, 10, 8

Sagot :

Answer:

1.2

Step-by-step explanation:

First, we need to find the mean of the data. We do this by adding all of the given numbers than dividing it by the number of numbers given. For example, we will add 9+7+11+10+8 which is 45. Since there are 5 given numbers, we are going to divide 45 by 5 which is 9. Now, we need to find the difference (subtraction) of all of the numbers in relation to 9. For example, for 9, we do 9-7 which is 2. Keep 2 in mind. Then we do 11-9 which is also 2. 10-9 is 1. 9-9 is 0. And finally, 9 minus 8 is also 1. Then, like what we did before, we need to find the mean of all of these differences. 2 plus 2 plus 1 plus 0 plus 1 is 6. Then, we divide 6 (our total of these differences) by 5 (the number of differences) 6 divided by 5 is 1.2 so there is your MAD and answer.

The mean absolute deviation of the given data is 1.2.

What is mean absolute deviation?

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.

Here's how to calculate the mean absolute deviation.

Data given: 9, 7, 11, 10, 8

Step 1: Calculate the mean.

[tex]mean = \frac{sum\ of\ observations}{number\ of\ observations} \\\\mean = \frac{9 + 7+11 + 10 + 8}{5}\\ \\mean =9[/tex]

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

Data    Distance from mean

9          |9 - 9| = 0

7          |7 - 9| = 2

11          |11 - 9| = 2

10         |10 - 9| = 1

8          |8 - 9| =1

Step 3: Add those deviations together.

Sum of deviations =  0 + 2 + 2 + 1 + 1 = 6

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

Mean absolute deviation = [tex]\frac{sum\ of\ deviations}{number\ of\ observations}\\ \\[/tex] = [tex]\frac{6}{5} = 1.2[/tex]

Learn more about mean absolute deviation here

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