There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.

Correct Option

Statement 1 is correct.

• Class A has student scores ranging from 17 to 21.
• Class B has student scores ranging from 22 to 30.
• When four students are shifted from Class A to Class B, their individual scores will be within the range of 17 to 21.
• Crucially, the highest possible score for a student from Class A (21) is lower than the lowest possible score for a student in Class B (22).
• Therefore, any student transferred from Class A to Class B will have a score lower than the existing average score of Class B.
• The addition of observations with values lower than the current average to a dataset will invariably decrease the overall average. Hence, the average score of Class B will definitely decrease.

Incorrect Options:

Statement 2 is incorrect.

• Four students are shifted from Class A. The effect on Class A's average score depends entirely on the scores of these four specific students relative to the original average score of Class A.
• If the four students who left Class A had scores below the original average of Class A, the average score of the remaining students in Class A would increase.
• Conversely, if the four students who left Class A had scores above the original average of Class A, the average score of the remaining students in Class A would decrease.
• If the four students who left Class A had scores equal to the original average of Class A, the average score of the remaining students would remain unchanged.
• Since the specific scores of the four students transferred are not provided, it cannot be definitively concluded that the average score of Class A will definitely increase.