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Data set \(T\) consists of a certain number of even integers divisible by 3. Is standard deviation of \(T\) positive?
(1) All elements of data set \(T\) are positive.
(2) The range of data set \(T\) is 0.
(1) All elements of data set \(T\) are positive.
(2) The range of data set \(T\) is 0.
16 Sep 2014, 01:23
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Official Solution:
Data set \(T\) consists of a certain number of even integers divisible by 3. Is standard deviation of \(T\) positive?
The standard deviation is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values. In essence, the standard deviation can be thought as a measure of the distance from the mean and since the distance cannot be negative, the standard deviation cannot be negative, meaning that it must be greater than or equal to zero: \(SD\geq0\).
Next, the standard deviation of a set is zero if and only if the set consists of identical numbers (or which is the same if the set consists of only one number).
(1) All elements of data set \(T\) are positive.
Set \(T\) can be {6, 6} so with the standard deviation equal to zero or {6, 12} so with the standard deviation more than zero. Not sufficient.
(2) The range of data set \(T\) is 0.
In order the range to be zero set \(T\) should have all identical elements, which means that the standard deviation of the set is zero. Sufficient.
Answer: B
Data set \(T\) consists of a certain number of even integers divisible by 3. Is standard deviation of \(T\) positive?
The standard deviation is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values. In essence, the standard deviation can be thought as a measure of the distance from the mean and since the distance cannot be negative, the standard deviation cannot be negative, meaning that it must be greater than or equal to zero: \(SD\geq0\).
Next, the standard deviation of a set is zero if and only if the set consists of identical numbers (or which is the same if the set consists of only one number).
(1) All elements of data set \(T\) are positive.
Set \(T\) can be {6, 6} so with the standard deviation equal to zero or {6, 12} so with the standard deviation more than zero. Not sufficient.
(2) The range of data set \(T\) is 0.
In order the range to be zero set \(T\) should have all identical elements, which means that the standard deviation of the set is zero. Sufficient.
Answer: B
General Discussion
nishantsharma87
Joined: 10 Oct 2013
Last visit: 12 Jan 2016
Posts: 15
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Location: India
Concentration: International Business, Technology
Schools: Guanghua '17 (A$) CKGSB '18 (A$)
GMAT 1: 620 Q39 V35
GMAT 2: 710 Q47 V40
WE:Sales (Computer Hardware)
28 Nov 2015, 03:49
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I think this is a high-quality question and I agree with explanation.
