Final answer:
Set A has a greater spread indicated by its interquartile range (IQR) of 32, compared to Set B which has an IQR of 31. This shows that Set A has a wider spread or more variability in the middle 50 percent of its data.
Step-by-step explanation:
To determine which data set has a greater spread, we can use the interquartile range (IQR), which is a measure of how much the middle 50% of the data set is spread out. The IQR is found by subtracting the first quartile from the third quartile. First, we need to order each data set from smallest to largest and then find the quartiles.
For Set A: {12, 16, 18, 23, 38, 48, 55},
the first quartile (Q1) is the median of the first half: 16,
the second quartile (Q2, or median) is 23,
and the third quartile (Q3) is the median of the second half: 48.
So the IQR of Set A is Q3 - Q1 = 48 - 16 = 32.
For Set B: {12, 13, 24, 44, 56},
Q1 is 13,
Q2 is 24,
and Q3 is 44.
The IQR of Set B is Q3 - Q1 = 44 - 13 = 31.
Comparing the two IQRs, Set A with an IQR of 32 has a slightly greater spread than Set B with an IQR of 31. This indicates that Set A has more variability in its middle 50 percent of data compared to Set B.