The average score over the past 10 years for the 5th grade math test is 89.5. This year’s top 5th graders took the test and scored 89, 93, 91, and 87. Compared to the long-term class average, this year’s top 5th graders’ scores are precise but not accurate.
The correct answer and explanation is:
The correct answer is: True
To understand this statement, it is important to define the terms “precision” and “accuracy” in a statistical context. Precision refers to how close a set of numbers are to each other, while accuracy refers to how close a number or set of numbers is to a known or accepted value.
In this scenario, the long-term average score for the 5th grade math test is 89.5. The scores of this year’s top students are 89, 93, 91, and 87. These scores are relatively close to each other, with a narrow spread of values. The difference between the highest score (93) and the lowest score (87) is only 6 points. This consistency among the scores shows a high level of precision.
However, when evaluating accuracy, we must look at how close the average of these scores is to the long-term average of 89.5. The mean of the given scores is calculated as follows:
(89 + 93 + 91 + 87) / 4 = 360 / 4 = 90
The average score of 90 is very close to the long-term average of 89.5. The difference is only 0.5 points. Although this difference is small, it does not support the idea that the scores are not accurate. In fact, they are quite accurate. Therefore, the original statement is actually false based on this calculation.
But if the problem is asking whether the scores are precise but not accurate compared to the average, and the conclusion is that they are not exactly 89.5, some might interpret that as not accurate. However, because the average of 90 is only slightly off from 89.5, it would be more precise to say the scores are both precise and fairly accurate.
So, while the statement says “precise but not accurate,” the evidence shows the scores are both. Thus, the statement is false.