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Is the standard deviation of the set of measurements x1, x2,
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25 Jun 2012, 02:01
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The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ? (1) The variance for the set of measurements is 4. (2) For each measurement, the difference between the mean and that measurement is 2. Diagnostic Test Question: 31 Page: 25 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: Is the standard deviation of the set of measurements x1, x2,
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25 Jun 2012, 02:02
SOLUTIONIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (1) The variance for the set of measurements is 4. The variance is just the square of the standard deviation, so if \(variance=4\) then \(SD=\sqrt{4}=2\). Sufficient. (2) For each measurement, the difference between the mean and that measurement is 2. So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient. Answer: D. For more on that subject check: Math Book chapter on SD  mathstandarddeviation87905.htmlPS questions on SD  psquestionsaboutstandarddeviation85897.htmlDS questions on SD  latelymanyquestionswereaskedaboutthestandard85896.html
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Re: Is the standard deviation of the set of measurements x1, x2,
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26 Jun 2012, 14:31
is SD < 3/
st. 1) SD = square root of variance (4) = 2 sufficient
st.2.) 2 <3 sufficient
Answer D



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Re: Is the standard deviation of the set of measurements x1, x2,
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27 Jun 2012, 11:39
Its D.. 1)square root of variance is standard deviation.. so it will be 2.. that is less than 3 ..sufficient 2) s.d is 2 .. that is less than 3.. sufficient.. so D is the answer.. OA?????
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Re: Is the standard deviation of the set of measurements x1, x2,
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29 Jun 2012, 03:28
SOLUTIONIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (1) The variance for the set of measurements is 4. The variance is just the square of the standard deviation, so if \(variance=4\) then \(SD=\sqrt{4}=2\). Sufficient. (2) For each measurement, the difference between the mean and that measurement is 2. So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient. Answer: D. For more on that subject check: Math Book chapter on SD  mathstandarddeviation87905.htmlPS questions on SD  psquestionsaboutstandarddeviation85897.htmlDS questions on SD  latelymanyquestionswereaskedaboutthestandard85896.html
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Re: Is the standard deviation of the set of measurements x1, x2,
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29 Jun 2012, 03:55
Is the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ? (1) The variance for the set of measurements is 4. (2) For each measurement, the difference between the mean and that measurement is 2. 1 Statement: s.deviation = sqrt(variance) = > thus, the std is 2. Sufficient; 2 Statement: The standard deviation cannot be greater than the difference of observation and the mean of the population, (take min and max of the population compare to mean). Thus, we can safely assume that the std is less than 3. Sufficient. Post Kudos, if you like my post.



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Re: Is the standard deviation of the set of measurements x1, x2,
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19 Sep 2012, 01:15
Hi Bunuel, I am of the opinion that calculation is not needed to prove D is sufficient. Standard deviation of an observation is how far it is from the mean of the observations. so by definition of SD, D is sufficient.. Please correct me if my understanding is wrong. Regards, Sach
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Re: Is the standard deviation of the set of measurements x1, x2,
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19 Sep 2012, 22:23
Bunuel wrote: SOLUTIONIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (1) The variance for the set of measurements is 4. The variance is just the square of the standard deviation, so if \(variance=4\) then \(SD=\sqrt{4}=2\). Sufficient (2) For each measurement, the difference between the mean and that measurement is 2. So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient. Answer: D. For more on that subject check: Math Book chapter on SD  mathstandarddeviation87905.htmlPS questions on SD  psquestionsaboutstandarddeviation85897.htmlDS questions on SD  latelymanyquestionswereaskedaboutthestandard85896.html Learned a new thing today



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Re: Is the standard deviation of the set of measurements x1, x2,
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20 Sep 2012, 01:06
I am of the opinion that calculation is not needed to prove D is sufficient. Standard deviation of an observation is how far it is from the mean of the observations. so by definition of SD, D is sufficient.. Please correct me if my understanding is wrong. Regards, Sach
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Re: Is the standard deviation of the set of measurements x1, x2,
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24 Jan 2013, 04:33
For 2 to hold good, say mean is 4 and for each of the 20 measurements to have a difference of 2 from the mean, all the measurements have to be either 2 or 6. . Please correct me if my understanding is not correct.
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Is the standard deviation of the set of measurements x1, x2,
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25 Dec 2016, 21:53
Nice Official Question. Here is what i did on this Question=> We need to see if the SD is less than 3 or not.
Statement 1> Variance =4 Hence SD=2
Hence Sufficient
Statement 2=> Using the equation => S.D = \(\sqrt{\frac{\sum(Meanx_i)^2}{N}}\) S.D => 2 Hence Sufficient
Hence D
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Re: Is the standard deviation of the set of measurements x1, x2,
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31 Jan 2018, 12:00
For the second expression, given mxi = 2 does the SD= \sqrt{4/20} ? This does not equal 2, which is the answer stated in the thread



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Re: Is the standard deviation of the set of measurements x1, x2,
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31 Jan 2018, 22:04
AIJ248 wrote: For the second expression, given mxi = 2 does the SD= \sqrt{4/20} ? This does not equal 2, which is the answer stated in the thread Hi Each m  xi = 2, so there are twenty such 2's. So first we will find variance, and then find square root of that variance to get SD. To get variance, we need to square all the values of (m  xi), and then find their average. Since all (m  xi) are 2, their squares will be '4', and thus their average will also be '4'. So our variance is 4  it becomes same as first statement. SD = √variance = √4 = 2.



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Re: Is the standard deviation of the set of measurements x1, x2,
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22 Apr 2018, 03:19
Bunuel wrote: SOLUTIONIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (1) The variance for the set of measurements is 4. The variance is just the square of the standard deviation, so if \(variance=4\) then \(SD=\sqrt{4}=2\). Sufficient. (2) For each measurement, the difference between the mean and that measurement is 2. So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient. Answer: D. For more on that subject check: Math Book chapter on SD  http://gmatclub.com/forum/mathstandard ... 87905.htmlPS questions on SD  http://gmatclub.com/forum/psquestions ... 85897.htmlDS questions on SD  http://gmatclub.com/forum/latelymanyq ... 85896.html Bunuel can you please elaborate on second statement you say " So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient." but the question is asking if SD the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?[/b]



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Re: Is the standard deviation of the set of measurements x1, x2,
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22 Apr 2018, 20:39
dave13 wrote: Bunuel wrote: SOLUTIONIs the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (1) The variance for the set of measurements is 4. The variance is just the square of the standard deviation, so if \(variance=4\) then \(SD=\sqrt{4}=2\). Sufficient. (2) For each measurement, the difference between the mean and that measurement is 2. So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient. Answer: D. For more on that subject check: Math Book chapter on SD  http://gmatclub.com/forum/mathstandard ... 87905.htmlPS questions on SD  http://gmatclub.com/forum/psquestions ... 85897.htmlDS questions on SD  http://gmatclub.com/forum/latelymanyq ... 85896.html Bunuel can you please elaborate on second statement you say " So, we have that \(mx_i=2\), since N=20 then we know everything to calculate the standard deviation. Sufficient." but the question is asking if SD the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?[/b] \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). (2) says that \(mx_i=2\), so \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{2^2+2^2+...+2^2}{20}}=\sqrt{\frac{20*2^2}{20}}=2\).
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Re: Is the standard deviation of the set of measurements x1, x2, x3, x4, .
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25 Sep 2018, 11:06
Abhi077 wrote: Is the standard deviation of the set of measurements x1, x2, x3, x4, . . ., x20 less than 3 ? (1) The variance for the set of measurements is 4. (2) For each measurement, the difference between the mean (of all 20 measurements) and that measurement is 2.
\(L = \left\{ {{x_1}\,,\,\,{x_2}\,,\,\,{x_3}\,,\,\,\, \ldots \,\,\,,\,\,{x_{20}}} \right\}\) \({\sigma _L} = \sigma \,\,\mathop < \limits^? \,\,3\) \(\left( 1 \right)\,\,\,{\sigma ^{\,2}} = 4\,\,\,\,\,\mathop \Rightarrow \limits^{\sigma \,\, \geqslant \,\,0} \,\,\,\,\sigma \,\, = \,\,2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle\) \(\left( 2 \right)\,\,\,\left {{x_k}  \mu } \right = 2\,\,\,,\,\,\,\,1 \leqslant k \leqslant 20\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\sigma ^{\,2}} = \,\,\,\frac{1}{{20}}\,\, \cdot \,\,\sum\limits_{k = 1}^{20} {\,\,{{\left( {\left {{x_k}  \mu } \right} \right)}^2}\,\,\, = } \,\,\,\frac{1}{{20}}\left( {20 \cdot 4} \right)\,\,\, = 4\) Hence \(\,\,\, \left( 2 \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left( 1 \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\) The correct answer is therefore (D). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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