To analyze the variation in the number of new followers for Ted and Millicent over the last 10 days, we can use the mean absolute deviation (MAD). The MAD measures the average distance between each data point and the mean of the data set. It's a useful way to understand how spread out the data points are.
1. Finding the Mean Absolute Deviation for Ted's Data:
Ted's follower data over the 10 days is: 101, 77, 65, 82, 113, 55, 66, 73, 88, 91.
The MAD for Ted's data is calculated to be:
[tex]$ \text{MAD for Ted} = 13.9 $[/tex]
2. Finding the Mean Absolute Deviation for Millicent's Data:
Millicent's follower data over the 10 days is: 88, 80, 92, 75, 120, 61, 101, 78, 83, 99.
The MAD for Millicent's data is calculated to be:
[tex]$ \text{MAD for Millicent} = 12.3 $[/tex]
3. Comparing the Mean Absolute Deviations:
To determine which data set is more varied, we compare the MAD values of Ted's and Millicent's data.
Since the MAD for Ted's data (13.9) is greater than the MAD for Millicent's data (12.3), we conclude that:
[tex]$ \text{Ted's data is generally more varied than Millicent's data.} $[/tex]
Filling in the blanks:
The mean absolute deviation of Ted's data is 13.9
The mean absolute deviation of Millicent's data is 12.3
Comparing the mean absolute deviations for Ted's and Millicent's data sets indicates that Ted's data is generally more varied than Millicent's data.
