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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If sets A and B have the same number of terms, is the standa ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If sets A and B have the same number of terms, is the standa ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B? (1) The range of set A is greater than the range of set B. (2) Sets A and B are both evenly spaced sets. OA C Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B? (1) The range of set A is greater than the range of set B. (2) Sets A and B are both evenly spaced sets. Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased: Do the values in set A deviate more from the mean than the do values in set B? Let SD = standard deviation. Statement 1: We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B. But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean. INSUFFICIENT. Statement 2: When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median. For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this: ...m-6, m-4, m-2, m, m+2, m+4, m+6... But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example: If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD. If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD. INSUFFICIENT. Statements 1 and 2: A and B have the same number of values. A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean. The range in A is greater. For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out. Thus, the values in A are deviating more from the mean, and A has a larger SD. SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B? (1) The range of set A is greater than the range of set B. (2) Sets A and B are both evenly spaced sets. Source: Veritas Prep $$\# A = \# B$$ $${\sigma _A}\mathop > \limits^? {\sigma _B}$$ $$\left( 1 \right)\,\,{R_A} > {R_B}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,1} \right\}\,,\,\,B = \left\{ {0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left\{ \matrix{ {\rm{A = }}\left\{ {0,0,0,10} \right\}\,\, \hfill \cr B = \left\{ {0,0,9,9} \right\}\,\, \hfill \cr} \right.\,\, \Rightarrow \,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$ $$\left( 2 \right)\,\,{\rm{finite}}\,\,{\rm{APs}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,2,4} \right\}\,,\,\,B = \left\{ {0,1,2} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,1,2} \right\}\,,\,\,B = \left\{ {0,2,4} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,{\rm{distance}}\,\,{\rm{between}}\,\,{\rm{terms}}\,\,{\rm{and}}\,\,{\rm{mean}}\,\,{\rm{in}}\,\,A\,\,{\rm{is}}\,\,{\rm{larger}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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