My question : is it possible to estimate the distribution of a data set using general statistical information about the said set?


Exemple :
Mean = 20
Median = 15
Standard Deviation = 2.5
Values range from 5 to 30
There are 20 values in the data set.

With that known, is it possible to determine how many values are above 25?


The exemple above is arbitrary, but shows more precisely what I meant when talking about "Estimating Non-Normal Distributions"

I do not need a graphical display, but rather a way to determine or estimate with the information available to me how many values are above or below "x".
If it is possible, what would be the best way to do it?

Thank you, will donate to the one who helped me!

This post was edited by WilliamKIDS on Jan 6 2015 03:33pm

how are you defining "estimate"?

you can start with the formulas for each piece of information you have and combine what you know to come up with a list of possible answers; especially if the data are integers since there will be finitely many data sets. then look at the possible data sets and it gives you a list of possible answers. but that's not "estimating".

/edit: i didn't bother trying to prove if there are multiple possible data sets, but im guessing there are. if there's only a single possible data set that fits all the criteria, then there you go.

shouldn't be too difficult to write a program to generate the possible data sets if the input are integers.

This post was edited by carteblanche on Jan 6 2015 04:07pm

the data are not necessarily integers.


my problem is not to generate possibilities of data sets but rather the most plausible one taking in account the standard deviation.

Hope that clear up a little bit my (wrongly used) definition of estimate, thank you.

i dont understand what you're trying to get. if two different data sets have the same standard deviation, mean, and median, then how are you defining one to be more "plausible" than the other? what class is this for? might help narrow down what you're trying to do. or do you have a context for this?

if there's only one dataset that fits your criteria, then your solution is simple. or if there are multiple data sets, but the same distribution for whatever you're looking for, eg x > 25

This post was edited by carteblanche on Jan 6 2015 08:32pm

this is not really for a class, but to give you a context, those would be the results of students to a certain class.

a data set with a median equal to the mean should follow Chebyshev inequality (http://en.wikipedia.org/wiki/Chebyshev%27s_inequality)
but i want my data set to be to most plausible ; the further you are from the mean, the less values there are

the answer is yes... the fraction above 25 is integral from u(t(25)) to infinity of the u(t), where t is teh t test value, which gives a fraction of people above 25. This can then be multiplied by the number of people in the sample to find the number of people above 25