To find the maximum possible range for each group when the members of the group \(73, 49, 32, 84, 39, 63, 22, 12\) are randomly assigned to two groups, we first need to determine the overall range of the entire group.
The range is calculated as the difference between the maximum and minimum values in the dataset.
- The maximum value (max) from the group is \(84\).
- The minimum value (min) from the group is \(12\).
Thus, the range of the entire group is:
\[ \text{Range} = \text{max} - \text{min} = 84 - 12 = 72 \]
When the members are divided into two groups, for both groups to have a range less than a certain value, each group's range must be less than half of the total range of the group.
To find the upper limit for the range of each group, we calculate half of the total range:
\[ \text{Half of the total range} = \frac{72}{2} = 36 \]
Therefore, for both groups to have a range less than this value when divided, the ranges need to be < 36.
However, we are seeking the value proposed in the options given. The highest range that both groups can still keep is determined by the provided options which are \(46.75, 61, 72, 44\).
The appropriate value would be less than 72, which is the overall range; hence, the correct maximum possible range for each group should allow for each group to be still below that limit.
Among the options, the one which is less than 72 is \(61\).
So, each group's range would need to be less than 61.