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There are a lot of products. Is the standard deviation of the prices o

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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There are a lot of products. Is the standard deviation of the prices o [#permalink]

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21 Apr 2017, 00:27
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65% (hard)

Question Stats:

39% (01:04) correct 61% (01:06) wrong based on 66 sessions

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There are a lot of products. Is the standard deviation of the prices of the products less than $60? 1) The median value of their price is$100
2) The range of their price is $110 [Reveal] Spoiler: OA _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons - try it yourself See our Youtube demo Senior Manager Joined: 02 Mar 2017 Posts: 271 Location: India Concentration: Finance, Marketing Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] Show Tags 21 Apr 2017, 19:56 I am Not sure whether i am Right....There a rule suggesting STD Should be approximately equal to One fourth the value of the range... Here Range is 110 So STD will be less than 60... statement 1 tells next to nothing.. Hence B _________________ Kudos-----> If my post was Helpful Manager Joined: 17 May 2015 Posts: 210 Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] Show Tags 21 Apr 2017, 22:58 1 This post received KUDOS VyshakhR1995 wrote: I am Not sure whether i am Right....There a rule suggesting STD Should be approximately equal to One fourth the value of the range... Here Range is 110 So STD will be less than 60... statement 1 tells next to nothing.. Hence B Hi VyshakhR1995, To be precise Standard deviation of any data set will always be less than equal to Range/2. I'll demonstrate it with a small example. consider two numbers 6 and 10. 1. Find the mean. (6+10)/2 = 8 2. Take the difference from the mean. 8 - 6 = 2 , 10 - 8 = -2 3. Square the difference. 2^2 = 4, (-2)^2 = 4 4. Take the mean of the squares of the difference from the mean. => (4+ 4)/2 = 4 5. Take the square root of step 4 result. => $$\sqrt{4} = 2$$ Standard deviation = 2 Range = 10 - 6 = 4 . In this case, SD is equal to Range/2. But if you insert any other element within this range, then SD will further decrease. => Standard deviation <= Range/2 Thanks. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 4880 GPA: 3.82 Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] Show Tags 24 Apr 2017, 01:46 1 This post received KUDOS Expert's post ==> If you modify the original condition and the question, you get standard deviation(d)≤range/2. Then, from d≤range/2=$110/2=$55<$60, it is always yes and sufficient.

Therefore, the answer is B.
Answer: B
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Re: There are a lot of products. Is the standard deviation of the prices o   [#permalink] 24 Apr 2017, 01:46
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