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21 Jul 2007, 02:47
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Hi,
Just wanted to understand the relation between Standard deviation and the Range for a set of numbers.
The standard deviation shows the amount of deviation across the mean value. Hence a larger S.D. would mean that there are more diverse set of values which are further away from the mean.
Hence,Doesnt a larger range signify a larger S.D. ?? Or, do we need to know the number of values in the set to reach to such a conclusion ? Shouldn't S.D. be independent of the number of digits in the Sequence ?
e.g. A Standard Deviation for a set with range of 20, should be larger than the S.D. for a set with range of 10.. Whatever maybe the number of digits in each range ?
Thanks for the help
Just wanted to understand the relation between Standard deviation and the Range for a set of numbers.
The standard deviation shows the amount of deviation across the mean value. Hence a larger S.D. would mean that there are more diverse set of values which are further away from the mean.
Hence,Doesnt a larger range signify a larger S.D. ?? Or, do we need to know the number of values in the set to reach to such a conclusion ? Shouldn't S.D. be independent of the number of digits in the Sequence ?
e.g. A Standard Deviation for a set with range of 20, should be larger than the S.D. for a set with range of 10.. Whatever maybe the number of digits in each range ?
Thanks for the help
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21 Jul 2007, 07:02
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in a general sense, standard deviation is "on average" how far the numbers deviate from the mean. anytime there is "on average" the number of values plays a part.
let's say there is a set of 999999 numbers. the mean is 5 and 999998 of the numbers are in fact 5. but 1 of the numbers is like - 50 and another is 60. the range is gigantic, however, the SD will be some really really really tiny number waaaaaay below 1 and near 0 because 999998 of the values don't deviate at all from the mean. (check out the equation for SD)
let's say there is another set of 2 numbers, 0 and 10. the mean is 5, the range is much smaller, but the SD is a whopping 5.
so when talking about range. it only tells you about two values. in a set you can have a billion numbers where only 2 are different, but are very different.
--- always think extreme and limits ---
let's say there is a set of 999999 numbers. the mean is 5 and 999998 of the numbers are in fact 5. but 1 of the numbers is like - 50 and another is 60. the range is gigantic, however, the SD will be some really really really tiny number waaaaaay below 1 and near 0 because 999998 of the values don't deviate at all from the mean. (check out the equation for SD)
let's say there is another set of 2 numbers, 0 and 10. the mean is 5, the range is much smaller, but the SD is a whopping 5.
so when talking about range. it only tells you about two values. in a set you can have a billion numbers where only 2 are different, but are very different.
--- always think extreme and limits ---
23 Jul 2007, 23:56
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Thanks HavoK_MAT for the explanation.
Just one more thing.. Do u feel that there will be a case where the Standard deviation is larger than the Range ??
Didnt get the last part about 2 numbers 0 and 10..
Just one more thing.. Do u feel that there will be a case where the Standard deviation is larger than the Range ??
Didnt get the last part about 2 numbers 0 and 10..
