Question

The median grade on a math test is 73, with a range of 68. However, during a flu epidemic, only 8 out of the 22 students in the class take the second test. The median grade on the second test is 61, and surprisingly, the range remains at 68. The students collectively conclude that the second test was no more challenging than the first one. In light of this, the median grade on the second test is MOST LIKELY lower because:

a) The flu epidemic affected a significant number of students.
b) The range indicates a wider spread of grades.
c) The reduced sample size may have impacted the median.
d) The second test was intentionally made more difficult.

Answer 1

The correct answer is option a) The flu epidemic affected a significant number of students.

Step-by-step explanation:

The most likely reason the median grade on the second test was lower is the flu epidemic that affected a significant number of students, not a change in the test's difficulty.

This is likely the primary reason the median grade on the second test was lower. Despite the range being equal for both tests, indicating that the spread of the grades was the same, the diminishing number of students taking the test due to the flu could have skewed the median downward. Reasons b) and c) are not as likely because the range did not change and the sample size, while smaller, does not inherently cause the median to drop. Option d) is speculative and not supported by the information provided that the range remained constant.

When calculating the median, we arrange the grades in ascending order and find the middle value. In the first test, there were 22 students, so the middle value was the 11th grade. However, during the flu epidemic, only 8 students took the second test. This reduced sample size means that the middle value in the second test is now the 4th grade. Therefore, the median grade on the second test is most likely lower because there are fewer grades higher than the middle value.