rakeshd347 wrote:For a certain exam, was the standard deviation of the scores for students U, V, W, X, Y, Z less than the standard deviation of the scores for students A B and C?
1. The standard deviation of the scores of students U V and W was less than the standard deviation of the scores of the students A B and C on the exam
2. The standard deviation of the scores of students X Y and Z was less than the standard deviation of the scores of the students A B and C on the exam
For this question, we can use the fact that when all values are equal, the standard deviation = 0.
Target question: Was the standard deviation of the scores for students U, V, W, X, Y, Z less than the standard deviation of the scores for students A B and C?
Statement 1: The standard deviation of the scores of students U V and W was less than the standard deviation of the scores of the students A B and C on the exam
There are several sets of scores that satisfy this condition. Here are two:
Case a:
U = V = W = 0, X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z greater than the standard deviation of A B and C.
Case b:
U = V = W = X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z less than the standard deviation of A B and C.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The standard deviation of the scores of students X Y and Z was less than the standard deviation of the scores of the students A B and C on the exam
There are several sets of scores that satisfy this condition. Here are two:
Case a: U = V = W = 0,
X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z greater than the standard deviation of A B and C.
Case b: U = V = W =
X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z less than the standard deviation of A B and C.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are still several sets of scores that satisfy this condition. Here are two:
Case a: U = V = W = 0, X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z greater than the standard deviation of A B and C.
Case b: U = V = W = X = Y = Z = 100, and A = 1, B = 2, C = 3. In this case,
the standard deviation of U, V, W, X, Y, Z less than the standard deviation of A B and C.
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
