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21 Sep 2023, 01:30
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D
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49%
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What is the standard deviation of set X, which contains consecutive odd integers?
(1) X consists of 10 terms.
(2) The range of X is 18.
(1) X consists of 10 terms.
(2) The range of X is 18.
21 Sep 2023, 21:06
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Bunuel
Given: Set X contains consecutive integers
Statement 1
(1) X consists of 10 terms.
Let's take an example to understand if this statement is sufficient to determine the SD.
Assume X had only 4 terms ➔\( X =\) {-1, 1, 3, 5}
The arithmetic mean of the above set is X = 2. We can find the distance of each term from 2 and use the calculated distance to find the standard deviation of the set. The standard deviation will depend on the distance of each member of the set from the mean and the number of terms in the set.
Now, let's add a constant value, say 10, to each term to arrive at a new set \(X_1 =\) {9, 11, 13, 15}. The arithmetic mean of this set is 12, however, the distance of each element of the set from the arithmetic mean doesn't change. Hence, the set \(X_1\) and \(X\) have the same value of SD.
In a nutshell, given the information in the premise, if we know the number of terms, we can find a unique value of SD of the set. This information is sufficient and we eliminate B, C, and E.
Statement 2
(2) The range of X is 18
We know from the premise, that X contains consecutive odd integers. Statement 2 provides the range of X. Therefore we can find the number of terms that are present in the set.
As the number of terms is known, we can find the SD of the set.
This information is also sufficient.
Option D
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