7.05 Mean absolute deviation (MAD)
Describe what the mean absolute deviation represents.
Consider the following set of values:2,\,8,\,6,\,3,\,10,\,15,\,6,\,6
Find the mean.
Complete the table of values, finding the distance of each value from the mean.
| Value | 2 | 8 | 6 | 3 | 10 | 15 | 6 | 6 |
|---|---|---|---|---|---|---|---|---|
| Distance from the mean |
Now, find the mean absolute deviation.
Consider the following set of values:3,\,12,\,24,\,2,\,40,\,10,\,9,\,4
Find the mean.
Complete the table of values, finding the distance of each value from the mean.
| Value | 3 | 12 | 24 | 2 | 40 | 10 | 9 | 4 |
|---|---|---|---|---|---|---|---|---|
| Distance from the mean |
Now, find the mean absolute deviation correct to two decimal places.
Consider the following set of values:2,\,10,\,12,\,4,\,24,\,20
Find the mean.
Complete the table of values, finding the distance of each value from the mean.
| Value | 2 | 10 | 12 | 4 | 24 | 20 |
|---|---|---|---|---|---|---|
| Distance from the mean |
Now, find the mean absolute deviation correct to two decimal places.
Consider the following set of values:399,\,185,\,236,\,654
Find the mean in exact value.
Now, find the mean absolute deviation.
Consider the following set of values:41,\,27,\,82,\,81,\,54,\,123
Find the mean.
Complete the table of values, finding the absolute difference of each value from the mean.
| Data | 41 | 27 | 82 | 81 | 54 | 123 |
|---|---|---|---|---|---|---|
| Absolute difference |
Now, find the mean absolute deviation correct to two decimal places.
Consider the following set of values:0,\,0,\,1,\,2,\,63,\,34,\,27,\,13
Find the mean.
Complete the table of values, finding the absolute difference of each value from the mean.
| Data | 0 | 0 | 1 | 2 | 63 | 34 | 27 | 13 |
|---|---|---|---|---|---|---|---|---|
| Absolute difference |
Now, find the mean absolute deviation correct to two decimal places.
The scores of five diving attempts by a professional diver are recorded below:5.7,\, 6.7,\, 6.5,\, 6.1,\, 6.5
Find the mean score correct to two decimal places.
Find the mean absolute deviation correct to two decimal places.
On the sixth attempt, the diver scores 9.9. How does this affect the mean and mean absolute deviation?
If each judge gave the diver the same score, determine the mean absolute deviation of the judges' scores.
Concerned that his heart rate was irregular, Derek’s doctor measured his heart rate (in beats per minute) 6 separate times in the space of an hour. They were as follows: 82,\, 95,\, 90,\, 95,\, 81,\, 94
Find the mean of these readings, correct to one decimal place.
The mean absolute deviation of beats per minute is 5.3. What does this mean?
Using the mean absolute deviation for average adult males as a reference, the doctor concluded that Derek’s heart rate was regular. What does this mean?
The windows to be fitted on a plane are produced on an assembly line and their thicknesses (in millimeters) are checked and recorded below:
| Window | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Thickness | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| Deviation from mean | ||||||||
| Absolute deviation |
Complete the table.
Find the mean thickness for the windows tested.
Find the mean absolute deviation for the windows tested.
A ninth window is tested for its thickness, and it is found to measure 6\text{ mm} in thickness. How does the greater thickness affect the mean?
How does the ninth measure of 6\text{ mm} in thickness affect the mean absolute deviation?
In a second round of testing, Window 4 was found to have a thickness of 4\text{ mm}. How does this affect the mean and the mean absolute deviation for the nine windows?