What is the standard deviation of set X, containing consecutive odd in

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