To find the mean absolute deviation, first find the mean and the absolute deviations. Then, find the mean of those deviations.
Mean Absolute Deviation: 2.8 Interpretation: The data is clustered close together.
Practice makes perfect
We have been asked to find and interpret the mean absolute deviation. To do so, we will find the mean and the absolute deviations first. Then, we will find the mean of those deviations. Let's start by calculating the mean. We will divide the sum of all of the data by the number of data points.
Sum of the Data:& 300
Number of Data Points:& 10
Mean:&300/10=30
Next, we need to find all of the absolute deviations, which are the distances between each data point and the mean value.
Data Point x
|30-x|
Absolute Deviation
24
|30- 24|
6
26
|30- 26|
4
28
|30- 28|
2
28
|30- 28|
2
30
|30- 30|
0
30
|30- 30|
0
32
|30- 32|
2
32
|30- 32|
2
34
|30- 34|
4
36
|30- 36|
6
Now that we know all of the absolute deviations, we need to add them all together. Then, we can find the average deviation by dividing the sum of the deviations by the number of deviations.
Sum of the Deviations:& 28
Number of Deviations:& 10
Mean:&28/10=2.8
Therefore, the mean absolute deviation is 2.8. Such a low value implies that the data is clustered close together.
