Question

If the members of the group {73,49,32,84,39,63,22,12} were randomly assigned to two groups, then each group’s range would need to be less than what value?(1 point)
Responses

72
72

44
44

46.75
46.75

61

Answer 1

To find the maximum range each group can have when the members of the group {73, 49, 32, 84, 39, 63, 22, 12} are randomly assigned to two groups, we need to calculate the overall range of the entire group and then determine how to split it into two groups such that each group's range is less than a certain value.

1. **Calculate the range of the entire group**:
- Maximum value = 84
- Minimum value = 12
- Range = Maximum - Minimum = 84 - 12 = 72

2. **Find the maximum range for each group**:
- When dividing into two groups, the sum of the ranges of the two groups must be less than the overall range. To ensure that both groups have a range lower than a certain value, we need a value that, when doubled, is greater than the overall range of 72.

If both groups need to have a range less than a certain value \( x \), then it follows that:

\[ 2x > 72 \]

This indicates:

\[ x > 36 \]

3. **Choose the options available**:
- 72
- 44
- 46.75
- 61

From the options provided, the value that is less than 72 and also satisfies \( x > 36 \) is any of the lower options.

Since the maximum possible range each group can have while ensuring that both groups are below the overall range while combined must be 36. Thus the maximum value for each group could be slightly below the halved total range.

The best answer according to the available options is:

**61**

This maintains the requirement that each group's range is less than 72, while still having both groups as per conditions allowed. Thus, the max range for each group must be less than 61.