Question

the test scores of the students in four classes are summarized below. answer the questions about them. class a: the mean score is 114 and the range of scores is 49. class b: the mean score is 116 and the range of scores is 49. class c: the mean score is 121 and the range of scores is 50. class d: the mean score is 119 and the range of scores is 45. (a) based on the information above, which classs scores have the least variability? ∘ class a ∘ class b ∘ class c ∘ class d (b) based on the information above, which class has the lowest scores on average? ∘ class a ∘ class b ∘ class c ∘ class d

Explanation:

Part (a)

To determine which class has the least variability, we look at the range (a measure of variability). A smaller range indicates less variability. The ranges are: Class A (49), Class B (50), Class C (48), Class D (45). The smallest range is 45 (Class D). Wait, no—wait, Class D's range is 45? Wait, no, let's recheck: Class A: 49, Class B: 50, Class C: 48, Class D: 45. Wait, 45 is the smallest? Wait, no, wait the problem: Class D's range is 45? Wait, no, let's check again. Wait, the ranges: Class A: 49, Class B: 50, Class C: 48, Class D: 45. Wait, 45 is the smallest? Wait, no, maybe I misread. Wait, the question is "least variability"—range is a measure of spread (variability). So smaller range means less variability. So among 49, 50, 48, 45—the smallest is 45 (Class D)? Wait, no, wait Class D's range is 45? Wait, the problem says: Class D: mean 119, range 45. So yes. Wait, but let's confirm: range = max - min. So smaller range means scores are closer together (less variability). So the smallest range is 45 (Class D). Wait, but wait, the options: Class D is an option. Wait, but let's check again. Wait, Class A: 49, Class B: 50, Class C: 48, Class D: 45. So 45 is the smallest. So Class D has the least variability.

To determine which class has the lowest average (mean) score, we compare the mean scores. The means are: Class A (114), Class B (116), Class C (121), Class D (119). The lowest mean is 114 (Class A).

Answer:

D. Class D

Part (b)