Standard Deviation

Ok, standard deviation.

I understand what it is and how to figure it out and the theory behind it.

I have an assignment which asks me to state a formula then apply it to some data ive gathered to find the standard deviation. While I understand how to figure it out, I have absolutely no clue how to use a formula for standard deviation. Ive looked up many and they all seem to be slightly different which confuses me. There also seems to be different formulas for if the data is from a sample or a population, which confuses me...

Can somebody please possibly guide me through how to work with standard deviation formulas?

Thanks

What kind of data do you have?

mmm4444bot said:

What kind of data do you have?

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I have 15 house prices.

289000, 400000 etc. etc.

Bolth_Mannn said:

I have an assignment which asks me to state a formula then apply it to some data ive gathered

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Your assignment seems general, in nature. If they have not discussed anything specific, then you're free to choose.


I don't know the context of your course, but this formula is used to estimate the standard deviation of a sample:



If you use it with your data, then it seems, to me, that you've completed the assignment. :cool:

mmm4444bot said:

..., but this formula is used to estimate the standard deviation of a sample:

View attachment 2178

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That denominator must be (N - 1), instead of N, for use in the formula for

the sample standard deviation.



Sources:

http://faculty.pittstate.edu/~winters/tutorial/StandardDeviation/index.html

https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php

http://www.une.edu.au/WebStat/unit_materials/c4_descriptive_statistics/standard_deviation.htm

Edited to reflect the correct denominator.

The formula that I posted is a guess, linked from Wikipedia. Wikipedia presents it as an uncorrected estimate of sample standard deviation; the version with 1/(N - 1) instead of 1/N is a corrected estimate.

I remain unable to determine exactly what the exercise calls for, but I'm thinking that any formula for standard deviation may suffice.

Absolute definition aside, as N increases - the % error due to "wrong" assumption decrease.

For example:

for n= 5 the error is 11.80%

for n= 10 the error is 5.4%

for n= 15 the error is 3.51%

for n= 30 the error is 1.71%

for n= 120 the error is 0.419%

In the prcalculator days, the sample size was frequently chosen to be 5 or 10. One of the big reason was that √(N-1) of those numbers are integer.

Subhotosh Khan said:

the sample size was frequently chosen to be 5 or 10. One of the big reason was that √(N-1) of those numbers are integer.

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Denis would concur.

My intro stats course taught that a minimum sample size of 23 is required, to give statistical analyses validity. I cannot recall the reason why, but that number stuck is stuck in memory.

I hope that the poster's course accepts any demonstrated use of a standard deviation formula.

JeffM said:

Actually, lookagain, none of your sources agrees with you.
They all use N - 1 rather than N + 1.

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Excellent. The original post was edited to correct the typo.

mmm4444bot said:

My intro stats course taught that a minimum sample size of 23
is required, to give statistical analyses validity. My intro courses have the minimum size at 30.
Less than a size of 30, the t-statistic chart/table kicks in.

I cannot recall the reason why, but that number stuck is stuck in memory.

I hope that the poster's course accepts any demonstrated use of a standard deviation formula.

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I hope the instructor makes clear which one he or she accepts. Then that student
won't have any excuses for using an incorrect formula (as I originally presented as a typo)
and get the correct value with the full credit.