exam_student Posted June 28, 2008 Share Posted June 28, 2008 Hi All, Is it safe to assume that if a range of set of numbers is larger, standard deviation of that set is higher? Is there a direct relation between range and standard deviation? (If it is so, it may help solving problems on std dev quickly) I searched the literature but didnt get any conclusive answer. Thanks and Regards. Quote Link to comment Share on other sites More sharing options...
flex_manny Posted June 28, 2008 Share Posted June 28, 2008 yes..in most cases the larger the range...the greater the standard deviation.... but more than that if you have the elements you want to look at how close the elements are from each other. Also, only if range = 0, is the standard deviation zero. Quote Link to comment Share on other sites More sharing options...
krovvidy Posted June 28, 2008 Share Posted June 28, 2008 Some useful SD related notes I made: 1. Calculation of Standard Deviation (SD): * Find the mean of the set of numbers * Find the difference between each of the numbers and the mean * Square the differences and add them together * Take the positive square root of this value 2. If you add/subtract a constant value K to/from all the numbers in a list, the arithmetic mean increases/decreases by K but the standard deviation remains the same. 3. If you multiply/divide all the numbers in the list by a constant value K, both the arithmetic mean and the standard deviation are multiplied/divided by K. 4. If mean = maximum value it means that all values are equal and SD is 0 5. A set of numbers with range of zero means that all of the numbers are the same, hence the dispersion of the numbers from its mean is zero 6. SD ranks the dispersion (deviation) of the numbers in a list. The more alike the numbers are, the less the dispersion, so the less the standard deviation. The more uneven members are dispersed around their arithmetic average, the more their SD 7. 16. If the range is 0, then the SD must also be 0, because there is no variance 8. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD 9. Standard deviation is how far the values spread out from the mean. A regular Bell Curve will always have 68% of the values within 1 SD, 95% of them within 2 SDs, and 99.7% within 3 SDs.High SD means the values are spread out; small SD means they're clustered closely around the mean. ... for more details: http://www.www.urch.com/forums/gmat-problem-solving/2424-baffling-standard-deviation-question-2.html 10. For comparing the SD for two sets any information about mean ,median,mode and range are insufficient unless you can determine the individual terms from the given data Quote Link to comment Share on other sites More sharing options...
exam_student Posted June 28, 2008 Author Share Posted June 28, 2008 Thanks flex_manny. Krovvidy, your list of points is a great help! Thanks. Quote Link to comment Share on other sites More sharing options...
800Bob Posted June 28, 2008 Share Posted June 28, 2008 Is it safe to assume that if a range of set of numbers is larger, standard deviation of that set is higher? Is there a direct relation between range and standard deviation? No, there is no direct relation between range and standard deviation. Range depends only on the two most extreme values, the smallest and the largest. Standard deviation is a measure of the dispersion of all the values. More often than not, the set that has the greater range will also have the greater SD, but not always. For example, take these two sets of data: Set A: 60, 80, 80, 80, 80, 100 Set B: 62, 62, 62, 98, 98, 98 Here Set A has the greater range, but set B has the greater SD. Quote Link to comment Share on other sites More sharing options...
exam_student Posted June 30, 2008 Author Share Posted June 30, 2008 thanks 800Bob. Quote Link to comment Share on other sites More sharing options...
ranjeet_1975 Posted July 2, 2008 Share Posted July 2, 2008 Thanks a lot Krovvidy for useful information. Quote Link to comment Share on other sites More sharing options...
Gmater-1 Posted July 8, 2008 Share Posted July 8, 2008 Thanks Bob for your insights Quote Link to comment Share on other sites More sharing options...
gmat731 Posted July 8, 2008 Share Posted July 8, 2008 If I have a SET of consecutive integers and I know the mean, is it possible to deduce the standard deviation? As per the notes from krovvidy it seems we need to know each individual values in the SET to calculate SD. Also there will be no relevance I guess with the bell curve, rt? Quote Link to comment Share on other sites More sharing options...
krovvidy Posted July 9, 2008 Share Posted July 9, 2008 If you have a set of consecutive integers, it's mean and no. of elements in the set, then you can calculated SD (because you can find out each element in the set by knowing the mean & no. of consecutive elements) ... so, it's the same as knowing all the elements in the set ... You can see this for yourself thru an example. HTH If I have a SET of consecutive integers and I know the mean, is it possible to deduce the standard deviation? As per the notes from krovvidy it seems we need to know each individual values in the SET to calculate SD. Also there will be no relevance I guess with the bell curve, rt? Quote Link to comment Share on other sites More sharing options...
bose Posted July 10, 2008 Share Posted July 10, 2008 If you have a set of consecutive integers, it's mean and no. of elements in the set, then you can calculated SD (because you can find out each element in the set by knowing the mean & no. of consecutive elements) ... so, it's the same as knowing all the elements in the set ... You can see this for yourself thru an example. HTH You do not need to know the mean only the number of elements is suff to calculate SD Quote Link to comment Share on other sites More sharing options...
getneonow Posted July 11, 2008 Share Posted July 11, 2008 did you miss one of the steps here? ? Some useful SD related notes I made: 1. Calculation of Standard Deviation (SD): * Find the mean of the set of numbers * Find the difference between each of the numbers and the mean * Square the differences and add them together * Divide the result by n (number of entries in the set) * Take the positive square root of this value Neo Quote Link to comment Share on other sites More sharing options...
synfist Posted November 25, 2008 Share Posted November 25, 2008 did you miss one of the steps here? ? Some useful SD related notes I made: 1. Calculation of Standard Deviation (SD): * Find the mean of the set of numbers * Find the difference between each of the numbers and the mean * Square the differences and add them together * Divide the result by n (number of entries in the set) * Take the positive square root of this value Neo I think it should be divide the results by (n-1) and not by n Calculation of Standard Deviation (SD): * Find the mean of the set of numbers * Find the difference between each of the numbers and the mean * Square the differences and add them together * Divide the result by n-1 * Take the positive square root of this value Quote Link to comment Share on other sites More sharing options...
fara0009 Posted April 1, 2009 Share Posted April 1, 2009 A Rough Estimate of s The standard deviation is not a very intuitive quantity, and so it is not always easy to tell if the value you calculate is reasonable (as opposed to being the ridiculous result of an arithmetic blunder). One rough estimate of the value of s arises out of the empirical rule. For approximately normally distributed populations, about 95% of the members will fall within two standard deviations of the mean, an interval with a width of 2 σ + 2 σ = 4 σ . Thus, particularly when sample sizes are not in the thousands (in which case there is a good likelihood of encountering members of the population that are three or more standard deviations from the mean), it is reasonable to equate this interval roughly with the sample range. This will give a ballpark estimate of σ and hence also of s. Thus, very roughly, for the data in a sample, we can write http://commons.bcit.ca/math/faculty/david_sabo/apples/math2441/section4/roughcuts/Image30.gif Quote Link to comment Share on other sites More sharing options...
navin Posted October 22, 2013 Share Posted October 22, 2013 No, there is no direct relation between range and standard deviation. Range depends only on the two most extreme values, the smallest and the largest. Standard deviation is a measure of the dispersion of all the values. More often than not, the set that has the greater range will also have the greater SD, but not always. For example, take these two sets of data: Set A: 60, 80, 80, 80, 80, 100 Set B: 62, 62, 62, 98, 98, 98 Here Set A has the greater range, but set B has the greater SD. ...................................................................................................................................................................................... If a given set of data is normally distributed in that case is there any relation between standard deviation and range. I think in that case there is relation between SD and Range. If we show data in Bell Curve than highest value is (mean+3SD) and the lowest data is (mean - 3SD). If we take the difference of {( mean+3SD) & (mean- 3SD)} it will give the value of range. So in data sufficiency questions if range is given for certain normal distribution we should be able to find SD. Please correct me if i am wrong !!!! Quote Link to comment Share on other sites More sharing options...
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