There are two Classes A and B having 25 and 30 students respectively In Class A the highest score is...........

Math and Mental Ability Average

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.

Consider the following statements:

1. The average score of Class-B will definitely decrease.

2. The average score of Class-A will definitely increase.

Which of the above statements is/are correct?

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Complete-Test, Previous year (2021)

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1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

Average = Sum of observations / Number of observations
Since 4 students are moved from A to B, therefore average of class B will definitely decrease as range of marks for class A is less than range of marks for class B. That is, the new students must be having less marks than the previous minimum marks of Class B.
Statement 1 is correct.
However, we cannot be sure regarding the marks of the 4 students that have been moved from class A. They may have marks close to 21, which will lead to decrease in the average marks of Class A. If they have marks close to 17, it will lead to increase in the average marks of Class A. Therefore, we cannot determine whether average of class A will increase or decrease. Statement 2 is incorrect.