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If the highest observation in the set S is 4 standard deviations above the mean and the lowest observation in the set is 5 standard deviations below the mean, what is the standard deviation of the set?
(1) The mean of the set is 24.
(2) The range of the set S is 72.
(1) The mean of the set is 24.
(2) The range of the set S is 72.
18 Feb 2026, 00:34
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As per the question:
H= M+4s ........(i)
L=M-5s ..........(ii)
(i)-(ii) ( subtracting (ii) from (i))
H-L=9s
s=(H-L)/9
Now, I will jump to the options:
Statement 1: M=24
I still played with it and by substituting it in the equation (i) and (ii) and still it wasn't enough
Statement 2:H-L=72
This clearly gives s
Answer: Option (B)
H= M+4s ........(i)
L=M-5s ..........(ii)
(i)-(ii) ( subtracting (ii) from (i))
H-L=9s
s=(H-L)/9
Now, I will jump to the options:
Statement 1: M=24
I still played with it and by substituting it in the equation (i) and (ii) and still it wasn't enough
Statement 2:H-L=72
This clearly gives s
Answer: Option (B)
19 Feb 2026, 05:22
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The question stem gives us a hidden relationship that makes this problem easier than it looks.
Let's call the mean μ and the standard deviation σ.
From the question stem:
• Highest observation = μ + 4σ
• Lowest observation = μ - 5σ
Principle: Range = Highest - Lowest
So: Range = (μ + 4σ) - (μ - 5σ) = 9σ
Notice that the mean cancels out! The range depends ONLY on σ.
Statement 1: The mean is 24.
This tells us μ = 24. But we still have no information about σ.
• If σ = 5, then Highest = 44, Lowest = -1
• If σ = 10, then Highest = 64, Lowest = -26
Both scenarios are valid, but give different values of σ.
→ NOT SUFFICIENT
Statement 2: The range is 72.
From our key insight: Range = 9σ
So: 9σ = 72
σ = 8
We found the standard deviation!
→ SUFFICIENT
Answer: B
Takeaway: Before evaluating statements, always simplify relationships from the question stem. Here, connecting "highest" and "lowest" to the range eliminated the mean variable entirely, making Statement 2 directly sufficient.
Let's call the mean μ and the standard deviation σ.
From the question stem:
• Highest observation = μ + 4σ
• Lowest observation = μ - 5σ
Principle: Range = Highest - Lowest
So: Range = (μ + 4σ) - (μ - 5σ) = 9σ
Notice that the mean cancels out! The range depends ONLY on σ.
Statement 1: The mean is 24.
This tells us μ = 24. But we still have no information about σ.
• If σ = 5, then Highest = 44, Lowest = -1
• If σ = 10, then Highest = 64, Lowest = -26
Both scenarios are valid, but give different values of σ.
→ NOT SUFFICIENT
Statement 2: The range is 72.
From our key insight: Range = 9σ
So: 9σ = 72
σ = 8
We found the standard deviation!
→ SUFFICIENT
Answer: B
Takeaway: Before evaluating statements, always simplify relationships from the question stem. Here, connecting "highest" and "lowest" to the range eliminated the mean variable entirely, making Statement 2 directly sufficient.
