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} has a greater spread because

Explanation:

Step1: Find range of Set A

Range = Max - Min. For Set A: {38, 12, 23, 48, 55, 16, 18}, Max = 55, Min = 12. So range = \( 55 - 12 = 43 \).

Step2: Find range of Set B

For Set B: {44, 13, 24, 12, 56}, Max = 56, Min = 12. So range = \( 56 - 12 = 44 \). Wait, no, wait, let's re - check Set A elements. Wait, Set A: 38,12,23,48,55,16,18. Max is 55, min is 12. Set B: 44,13,24,12,56. Max is 56, min is 12. Wait, but maybe I miscounted. Wait, Set A has 7 elements: 12,16,18,23,38,48,55. So max 55, min 12. Range 55 - 12 = 43. Set B: 12,13,24,44,56. Max 56, min 12. Range 56 - 12 = 44. Wait, but the initial thought was wrong. Wait, no, maybe the user made a typo? Wait, no, let's re - evaluate. Wait, maybe the sets are: Set A: {38, 12, 23, 48, 55, 16, 18}, Set B: {44, 13, 24, 12, 56}. Wait, but when we calculate the range, the range of a data set is a measure of spread. The range of Set A: 55 - 12 = 43. The range of Set B: 56 - 12 = 44. Wait, but that would mean Set B has a larger range. But wait, maybe I misread the sets. Wait, let's check again. Set A: 38,12,23,48,55,16,18. The values are 12,16,18,23,38,48,55. So the maximum is 55, minimum is 12. Set B: 44,13,24,12,56. Values:12,13,24,44,56. Max 56, min 12. So range of A: 55 - 12 = 43. Range of B: 56 - 12 = 44. So Set B has a greater spread (range) because its range (56 - 12 = 44) is greater than Set A's range (55 - 12 = 43).

Wait, but maybe I made a mistake in Set B's elements. Let's count Set B elements: 44,13,24,12,56. That's 5 elements. Set A has 7 elements. The range is a measure of spread. So to find which set has a greater spread, we can use the range (max - min).

For Set A:

• Identify the maximum value: In the set {38, 12, 23, 48, 55, 16, 18}, the maximum value is 55.
• Identify the minimum value: The minimum value is 12.
• Calculate the range: \( \text{Range}_A=55 - 12 = 43 \)

For Set B:

• Identify the maximum value: In the set {44, 13, 24, 12, 56}, the maximum value is 56.
• Identify the minimum value: The minimum value is 12.
• Calculate the range: \( \text{Range}_B = 56-12=44 \)

Since \( 44>43 \), Set B has a greater spread because its range (the difference between the maximum and minimum values) is greater.

Answer:

Set B has a greater spread because its range (calculated as maximum value minus minimum value) is greater. The range of Set A is \( 55 - 12 = 43 \) and the range of Set B is \( 56 - 12 = 44 \), and \( 44>43 \).