How can we use the concept:
Most often when finding Mean Absolute Deviation (henceforth called MAD), we follow a series of steps and not a formula.
Most often when finding Mean Absolute Deviation (henceforth called MAD), we follow a series of steps and not a formula.
The steps:
1) Find the mean of the data set.
2) Find the absolute deviation of each data point by finding the absolute value of the difference between each data point and the mean. (Since we are using absolute value, all these values will be positive.)
3) Find the mean of the deviations.
Sample Math Problems
1. Given the data set: 11, 6, 18, 4, 15, 25 find the mean absolute deviation.
Solution:
Step 1: Find the mean of the data set.
(11 + 6 + 18 + 4 + 15 + 25) 6 = 13.167 (answer rounded to the thousandths place)
Step 2: Find the absolute value of the difference of each data point from the mean.
| 11 - 13.167 | = 2.167
| 6 - 13.167 |= 7.167
| 18 - 13.167 |= 4.833
| 4 - 13.167 | = 9.167
| 15 - 13.167 |= 1.833
| 25 - 13.167 |= 11.833
Step 3: Find the mean of the deviations.
(2.167 + 7.167 + 4.833 + 9.167 + 1.833 + 11.833) 6 = 6.167
2. Given the data set: 30, 49, 17, 17, 46 find the mean absolute deviation.
Solution:
Step 1: Find the mean of the data set.
(30 + 49 + 17 + 17 + 46) 5 = 31.8
Step 2: Find the absolute value of the difference of each data point from the mean.
| 30 - 31.8 |= 1.8
| 49 - 31.8 |= 17.2
| 17 - 31.8 |= 14.8 We will use this twice in step 3 of solving since this data point occurs twice in the data set.
|46 - 31.8|= 14.2
Step 3: Find the mean of the deviations.
(1.8 + 17.2 + 14.8 + 14.8 + 14.2) 5 = 12.56
3. Given the data set: 81, 51, 54, 97, 68, 57, 64 find the mean absolute deviation.
Solution:
Step 1: Find the mean of the data set.
(81 + 51 + 54 + 97 + 68 + 64) 6 = 69.167
Step 2: Find the absolute value of the difference of each data point from the mean.
| 81 - 69.167 | = 11.833
| 51 - 69.167 | = 18.167
| 54 - 69.167 | = 15.167
| 97 - 69.167 |= 27.833
| 68 - 69.167 |= 1.167
| 64 - 69.167 |= 5.167
Step 3: Find the mean of the deviations.
(11.833 + 18.167 + 15.167 + 27.833 + 1.167 + 5.167) 6 = 13.22 (rounded)
4. Given the data set: 57, 45.3, 58.2, 46.7, 65.5 find the mean absolute deviation.
Solution:
Step 1: Find the mean of the data set.
(57 + 45.3 + 58.2 + 46.7 + 65.5) 5 = 54.54
Step 2: Find the absolute value of the difference of each data point from the mean.
| 57 - 54.54 |= 2.46
| 45.3 - 54.54 |= 9.24
| 58.2 - 54.54 |= 3.66
| 46.7 - 54.54 |= 7.84
|65.5 - 54.54 |= 10.96
Step 3: Find the mean of the deviations.
(2.46 + 9.24 + 3.66 + 7.84 + 10.96) 5 = 6.832
