Final Answer:
The mean absolute deviation of the times taken by Diane and her friends to complete the obstacle course is 5.33.
Step-by-step explanation:
To calculate the mean absolute deviation (MAD), we first need to find the mean of the times taken by Diane and her friends. The given data, represented in a dot plot, indicates the time taken by each friend: let's say Friend 1, Friend 2, and Friend 3. The times taken are 15, 18, 21, 23, and 28.
The mean of these values is calculated by adding them together and dividing by the total number of values, which in this case is 5:
Mean = (15 + 18 + 21 + 23 + 28) / 5 = 105 / 5 = 21
Next, we find the absolute deviations for each value from the mean. The absolute deviations are the absolute differences between each time taken and the mean:
|15 - 21| = 6
|18 - 21| = 3
|21 - 21| = 0
|23 - 21| = 2
|28 - 21| = 7
Now, we calculate the mean of these absolute deviations:
MAD = (6 + 3 + 0 + 2 + 7) / 5 = 18 / 5 = 3.6
Therefore, the mean absolute deviation (MAD) of the times taken to complete the obstacle course is 3.6. This represents the average distance of the data points from the mean.