The is the average of the of the differences between the and each value in the data set. Let's see the given data set.
| Prices of Tablets (dollars)
|
| 130
|
150
|
190
|
100
|
175
|
| 120
|
165
|
140
|
180
|
190
|
We will start by calculating the mean of the given set of numbers. We can see that there are 10 values in our data set. Let's calculate the mean!
Mean = Sum of values/Number of values
Mean = 130+150+190+100+175+120+165+140+180+190/10
Mean = 1540/10
Mean = 154
We found that the mean of the given data set is 154. We are ready to calculate the MAD. We noted before that the MAD of a set of data is the average of the absolute values of the differences between the mean and each value in the data set.
| x- x_1|+| x- x_2|+...+| x- x_n|/n
In this formula, x_1,...,x_n are the values in the set of data, x is the mean, and n is the number of values. We already know that x= 154 and n= 10. Let's use a table to find the sum of the absolute values of the differences.
| x_i
|
x-x_i
|
|x-x_i|
|
| 130
|
154- 130=24
|
|24|=24
|
| 150
|
154- 150=4
|
|4|=4
|
| 190
|
154- 190=-36
|
|-36|=36
|
| 100
|
154- 100=54
|
|54|=54
|
| 175
|
154- 175=- 21
|
|- 21|=21
|
| 120
|
154- 120=34
|
|34|=34
|
| 165
|
154- 165=-11
|
|-11|=11
|
| 140
|
154- 140=14
|
|14|=14
|
| 180
|
154- 180=-26
|
|-26|=26
|
| 190
|
154- 190=- 36
|
|- 36|=36
|
| Sum of Values
|
260
|
Finally, we need to divide by 10. This will give us the average.
Mean Absolute Deviation (MAD)
260/10=26
A MAD of 26 indicates that the data, on average, are 26 units away from the mean. In the context of the problem, this means that the prices of tablets, on average, are 26 dollars away from the mean 154.
