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23 Jan 2023, 02:30
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What is the standard deviation of set X, containing consecutive odd integers?
(1) Set consists of 10 elements
(2) The range of set is 18
(1) Set consists of 10 elements
(2) The range of set is 18
23 Jan 2023, 12:00
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Bunuel
A good question !
To understand the question question let's take an example =
Let's assume that a set consists of three elements which are equally spaced , i.e. the members of the set are in arithmetic progression
\(A_1\) = {\(x_1, \quad x_2, \quad x_3\)}
Assume that the SD of this set is "s". As the distance of each element of the set from the mean is constant we can compute the SD.
If we move each element of the set by a fixed constant the SD of the set doesn't change.
For example
\(A_2\) = {\(x_1+d, \quad x_2+d, \quad x_3+d\)}
The SD of the set \(A_2\) is also "s"
Hence in the case of a uniformly spaced set, the calculation of the SD doesn't depend on the actual value of the terms. If we know the number of terms in the set, and know the common difference we can find the SD of the set.
Statement 1
(1) Set consists of 10 elements
From the premise we know that the common difference between the terms = 2
Number of terms = 10
We can calculate the SD.
Note, this is a DS question, so we don't need to actually compute the value, but we can do so if required.
The statement is sufficient.
Statement 2
(2) The range of set is 18
As the range is given to us and we know that the difference between consecutive terms is 2, we can find the number of terms in the set.
Once the number of terms is known, we can find the SD.
The statement is sufficient.
Option D
06 Jul 2026, 09:03
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What is the standard deviation of set X, containing consecutive odd integers?
(1) Set consists of 10 elements
(2) The range of the set is 18
Answer: D — EACH statement ALONE is sufficient
Key Concept:
For a set of consecutive odd integers (e.g., 3, 5, 7, 9...), the common difference between terms is always fixed at 2. Standard deviation measures the spread of data, not the actual values themselves. Since the spacing between consecutive odd integers never changes, the standard deviation of such a set depends only on how many terms (n) it contains — not on which specific odd integer the set starts from.
Illustration:
Set A = {1, 3, 5} → n = 3
Set B = {101, 103, 105} → n = 3
Both sets have the exact same standard deviation because they have identical spacing—the entire set is just shifted. This confirms that SD is a function of n alone (for a fixed common difference).
Evaluating the Statements:
Statement (1): n = 10 elements
Since n is given directly, and the common difference is always 2, the standard deviation can be uniquely determined.
Sufficient
Statement (2): Range = 18 For a set of n consecutive odd integers:
2(n−1)=18 ⟹ n−1=9 ⟹ n=10
This also yields n = 10, which is enough to determine the standard deviation.
Sufficient
Both statements independently lead to n = 10, and since SD depends only on n (given the fixed common difference of 2), each statement alone is sufficient to answer the question.
Correct Answer: D
(1) Set consists of 10 elements
(2) The range of the set is 18
Answer: D — EACH statement ALONE is sufficient
Key Concept:
For a set of consecutive odd integers (e.g., 3, 5, 7, 9...), the common difference between terms is always fixed at 2. Standard deviation measures the spread of data, not the actual values themselves. Since the spacing between consecutive odd integers never changes, the standard deviation of such a set depends only on how many terms (n) it contains — not on which specific odd integer the set starts from.
Illustration:
Set A = {1, 3, 5} → n = 3
Set B = {101, 103, 105} → n = 3
Both sets have the exact same standard deviation because they have identical spacing—the entire set is just shifted. This confirms that SD is a function of n alone (for a fixed common difference).
Evaluating the Statements:
Statement (1): n = 10 elements
Since n is given directly, and the common difference is always 2, the standard deviation can be uniquely determined.
Sufficient
Statement (2): Range = 18 For a set of n consecutive odd integers:
2(n−1)=18 ⟹ n−1=9 ⟹ n=10
This also yields n = 10, which is enough to determine the standard deviation.
Sufficient
Both statements independently lead to n = 10, and since SD depends only on n (given the fixed common difference of 2), each statement alone is sufficient to answer the question.
Correct Answer: D
