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18 Dec 2024, 10:49
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Leonard's comic book collection received grades that are consecutive multiples of 5. We need to determine the standard deviation of these grades, where:
- 3 comic books received the lowest grade (G1).
- 5 comic books received the second-lowest grade (G2).
- 4 comic books received the second-highest grade (G3).
- x comic books received the highest grade (G4).
The grades are in the form of consecutive multiples of 5, such as \(G1 = a\), \(G2 = a+5\), \(G3 = a+10\), \(G4 = a+15\), where \(a\) is the lowest grade.
Now,
Statement (1): \(x = 2\)
- Knowing \(x\) helps us determine the total number of comic books: \(3 + 5 + 4 + 2 = 14\).
- The grades are fixed as consecutive multiples of 5, which allows us to determine their frequencies completely.
- Since the grades are consecutive multiples of 5, even without knowing \(a\), we can calculate the variance and standard deviation because changing \(a\) shifts all grades by the same amount, which does not affect their relative distances or the standard deviation.
- This statement is sufficient to calculate the standard deviation.
Statement (2): The lowest grade assigned to the comic books was 35.
- This statement gives us \(a = 35\), and so \(G1 = 35\), \(G2 = 40\), \(G3 = 45\), \(G4 = 50\).
- However, without knowing \(x\), we cannot determine the exact distribution of the grades. The total variance and standard deviation depend on the number of comic books that received each grade, particularly the highest grade.
- This statement alone is insufficient as it does not provide the number of books receiving the highest grade (\(x\)).
Conclusion:
- Statement (1) is sufficient to determine the standard deviation of the grades of Leonard's comic books.
- Statement (2) is insufficient on its own.
Correct Answer: A
- 3 comic books received the lowest grade (G1).
- 5 comic books received the second-lowest grade (G2).
- 4 comic books received the second-highest grade (G3).
- x comic books received the highest grade (G4).
The grades are in the form of consecutive multiples of 5, such as \(G1 = a\), \(G2 = a+5\), \(G3 = a+10\), \(G4 = a+15\), where \(a\) is the lowest grade.
Now,
Statement (1): \(x = 2\)
- Knowing \(x\) helps us determine the total number of comic books: \(3 + 5 + 4 + 2 = 14\).
- The grades are fixed as consecutive multiples of 5, which allows us to determine their frequencies completely.
- Since the grades are consecutive multiples of 5, even without knowing \(a\), we can calculate the variance and standard deviation because changing \(a\) shifts all grades by the same amount, which does not affect their relative distances or the standard deviation.
- This statement is sufficient to calculate the standard deviation.
Statement (2): The lowest grade assigned to the comic books was 35.
- This statement gives us \(a = 35\), and so \(G1 = 35\), \(G2 = 40\), \(G3 = 45\), \(G4 = 50\).
- However, without knowing \(x\), we cannot determine the exact distribution of the grades. The total variance and standard deviation depend on the number of comic books that received each grade, particularly the highest grade.
- This statement alone is insufficient as it does not provide the number of books receiving the highest grade (\(x\)).
Conclusion:
- Statement (1) is sufficient to determine the standard deviation of the grades of Leonard's comic books.
- Statement (2) is insufficient on its own.
Correct Answer: A
Bunuel
18 Dec 2024, 10:59
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Common difference is known i.e 5..Number of terms are required.
1. x=2 gives the total number of terms...SUFFICIENT
2 lowest grade =35..but number of terms is unknown.. NOT SUFFICIENT
Statement 1 alone sufficient
Answer A
1. x=2 gives the total number of terms...SUFFICIENT
2 lowest grade =35..but number of terms is unknown.. NOT SUFFICIENT
Statement 1 alone sufficient
Answer A
18 Dec 2024, 11:03
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Answer is A
Considering grades are x, x+5, x+10, x+15
Mean = [3*X + 5(X*5) + 4*(X+10) + 2*(X+15)]/14 will give me a value of X + 95/14
x will cancel out for each of the deviations x- (x-95/14) or x+5 -(x -95/14) to give me a concrete answer for standard deviation
however knowing 35 is the lowest grade I don't know what x is it could be 1 or 1000 which could vary my mean hence s.d. cannot be calculated
Considering grades are x, x+5, x+10, x+15
Mean = [3*X + 5(X*5) + 4*(X+10) + 2*(X+15)]/14 will give me a value of X + 95/14
x will cancel out for each of the deviations x- (x-95/14) or x+5 -(x -95/14) to give me a concrete answer for standard deviation
however knowing 35 is the lowest grade I don't know what x is it could be 1 or 1000 which could vary my mean hence s.d. cannot be calculated
Bunuel
