Question

select the correct answer from each drop - down menu. which data set has a greater spread? why? set a: {38, 12, 23, 48, 55, 16, 18} set b: {44, 13, 24, 12, 56} drop - down for which set has greater spread has a greater spread because drop - down options: it has more data values, its mean is greater, its median is greater, its range is greater

Explanation:

Step1: Calculate range of Set A

First, find the maximum and minimum of Set A: $\{38, 12, 23, 48, 55, 16, 18\}$. Max = 55, Min = 12. Range = $55 - 12 = 43$.

Step2: Calculate range of Set B

For Set B: $\{44, 13, 24, 12, 56\}$. Max = 56, Min = 12. Range = $56 - 12 = 44$.

Step3: Compare ranges

Set B's range (44) > Set A's range (43). Also, check other options: Both have 7 and 5 elements (so "more data" is wrong). Mean/median: Let's check mean. Set A mean: $\frac{38+12+23+48+55+16+18}{7}=\frac{210}{7}=30$. Set B mean: $\frac{44+13+24+12+56}{5}=\frac{149}{5}=29.8$. Median: Set A (sorted: 12,16,18,23,38,48,55) median 23. Set B (sorted:12,13,24,44,56) median 24. But range difference (44 vs 43) is clear, and "its range is greater" fits.

Answer:

Set A has a greater spread? No, wait. Wait, Set B's range is 44, Set A's is 43. Wait, the first dropdown: "Set A" or "Set B"? Wait, the problem says "Which data set has a greater spread? [dropdown] has a greater spread because [dropdown]". Wait, let's recheck. Wait, Set A: elements 38,12,23,48,55,16,18 (7 elements). Sorted: 12,16,18,23,38,48,55. Range: 55-12=43. Set B: 44,13,24,12,56 (5 elements). Sorted:12,13,24,44,56. Range:56-12=44. So Set B has greater range. So first dropdown: Set B. Second dropdown: "its range is greater".

So the answers are: First dropdown: Set B; Second dropdown: its range is greater.