Confidence intervals with a skewed histogram


Less is more. Stay pure. Stay poor.
Yes you should have concerns. You should attempt to normalize the data. Perhaps try and natural log transform the observations.


Ambassador to the humans
I would actually say that you're probably fine. You have a large enough sample size that the confidence interval should be trustworthy.

One might argue that the mean isn't the best measure of central tendency with a skewed data set but if it's what you're interested in then I think you're good to go.
I said

"Our data is skewed right, but the confidence interval is approximately valid because the central limit theorem states that the mean of a fairly large amount of independent values, will be approximately normally distributed.
Because we have a sample size of 541 values we can assume that the confidence interval is valid and indeed reflective of the true mean of the population.
If we wanted to have a more accurate CI, we should transform the data – with this skewed data set a natural log transformation would be very useful in normalising the data.

In regards to transforming the data - we were asked to transform it later on, the natural log proved the best to make it normally distributed.

Do you guys think my above answer is sufficient?

Thanks for both of your help by the way i appreciate it