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02 Jun 2026, 11:19
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The weights of 6 packages are 12, 10, 11, 10, 12, and 10 pounds, respectively. In which of the following intervals does the standard deviation of the weights of the packages lie?
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
02 Jun 2026, 15:51
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The weights of 6 packages are 12, 10, 11, 10, 12, and 10 pounds, respectively. In which of the following intervals does the standard deviation of the weights of the packages lie?
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
We have the following list in ascending order:
{10, 10, 10, 11, 12, 12}
The mean weight is 65/6 ≈ 11.
The absolute differences from the mean are approximately:
{≈1, ≈1, ≈1, ≈0, ≈1, ≈1}
The standard deviation measures how spread out the values are from the mean. Since the values differ from the mean by only about 1, the standard deviation is clearly less than 3.
Thus, the standard deviation lies between 0 and 3.
Answer: A.
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
We have the following list in ascending order:
{10, 10, 10, 11, 12, 12}
The mean weight is 65/6 ≈ 11.
The absolute differences from the mean are approximately:
{≈1, ≈1, ≈1, ≈0, ≈1, ≈1}
The standard deviation measures how spread out the values are from the mean. Since the values differ from the mean by only about 1, the standard deviation is clearly less than 3.
Thus, the standard deviation lies between 0 and 3.
Answer: A.
03 Jun 2026, 23:46
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kingbucky
Similar questions to practice:
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04 Jun 2026, 16:30
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The weights of 6 packages are 12, 10, 11, 10, 12, and 10 pounds, respectively. In which of the following intervals does the standard deviation of the weights of the packages lie?
The standard deviation of a group of values is basically the average of the absolute (positive) differences between the values and the mean of the values. Although, that's not the exact definition, it's sufficiently accurate for answering GMAT Standard Deviation questions.
So, to approximate the standard deviation, we can do the following:
Find the mean of the values:
Average = Sum/Number = 65/6 ≈ 11
Find the absolute difference between each value and the mean:
|12 - 11| = 1
|10 - 11| = 1
|11 - 11| = 0
|10 - 11| = 1
|12 - 11| = 2
|10 - 11| = 1
Just scanning the differences, we see that all are less than 3. So, without even calculating the average difference, we can see that choice (A) Between 0 and 3 must be correct.
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
Correct answer: A
The standard deviation of a group of values is basically the average of the absolute (positive) differences between the values and the mean of the values. Although, that's not the exact definition, it's sufficiently accurate for answering GMAT Standard Deviation questions.
So, to approximate the standard deviation, we can do the following:
Find the mean of the values:
Average = Sum/Number = 65/6 ≈ 11
Find the absolute difference between each value and the mean:
|12 - 11| = 1
|10 - 11| = 1
|11 - 11| = 0
|10 - 11| = 1
|12 - 11| = 2
|10 - 11| = 1
Just scanning the differences, we see that all are less than 3. So, without even calculating the average difference, we can see that choice (A) Between 0 and 3 must be correct.
(A) Between 0 and 3
(B) Between 6 and 7
(C) Between 8 and 10
(D) Between 10 and 11
(E) Between 11 and 12
Correct answer: A
