To determine which data set has a greater spread, we need to compute the range for each set. The range of a data set is the difference between the maximum value and the minimum value in the set.
Set A: {38, 12, 23, 48, 55, 16, 18}
1. Identify the maximum and minimum values in Set A:
- Maximum value: 55
- Minimum value: 12
2. Calculate the range of Set A:
[tex]\[
\text{Range of Set A} = \text{Maximum Value} - \text{Minimum Value} = 55 - 12 = 43
\][/tex]
Set B: {44, 13, 24, 12, 56}
1. Identify the maximum and minimum values in Set B:
- Maximum value: 56
- Minimum value: 12
2. Calculate the range of Set B:
[tex]\[
\text{Range of Set B} = \text{Maximum Value} - \text{Minimum Value} = 56 - 12 = 44
\][/tex]
Now, compare the ranges of the two sets:
- Range of Set A: 43
- Range of Set B: 44
Conclusion:
Set B has a greater spread because the range of Set B (44) is greater than the range of Set A (43).
So, the correct answer is:
Set B has a greater spread because the range of Set B is larger than the range of Set A.
