Thread: Estimating Mean & Standard deviation from a cumulative frequency curve

How would you go about estimating the mean and the standard deviation from a cumulative frequency curve, if the only data points you know for certain are the 10th, 50th and 90th percentile? I've determined that the distribution is right-skewed, but can't figure out how i would estimate the mean and the sd.

any help will be greatly appreciated!

Originally Posted by mathiscruel

How would you go about estimating the mean and the standard deviation from a cumulative frequency curve, if the only data points you know for certain are the 10th, 50th and 90th percentile? I've determined that the distribution is right-skewed, but can't figure out how i would estimate the mean and the sd.

any help will be greatly appreciated!

In what context has this arisen? If it is a home work problem what have you been covering? Do your notes say anything relevant?

I would consider fitting a beta distribution to the given quantiles (though that will still need some side assumptions), but that is not elementary and I will not do it here.

(a triangular distribution is probably easier to handle than the beta - look at the Wikipedia article on the triangular distribution for the cumulatve triangular distribution function.)

CB