# Can this be considered close to normally distributed?

I have a series of data looking like this, and I wonder if this can be considered to close to normally distributed, even if it has a tail to the right? Can I use t-tests and define "large" being over 1 standard deviation and such, or would that be wrong?

Count    1 536
Mean     27,8
Median   26,0
Mode     28,0
Stdv     14,4
Skew      0,9
Max      92,0
Min       0,0


Here is a histogram of the data: • There isn't enough information in this numerical summary to conclude, with any certainty, the shape of the distribution. We need a histogram and/or QQ plot of the data to answer this. The fact that there is little skew (although a skew of 0.9 in a sample size of 536 may indicate some problems) and the mean/median/mode are about about equal is a good sign but doesn't guarantee anything. This could be a very long-tailed (but roughly symmetric) distribution for all we know. Oct 9, 2012 at 13:12
• One indication of non-normality is that the mean and median, while close to each other, are far from the middle of the distribution which would be 46. One thing that could cause this is an outlier or two at the high end. 92 is $\frac{92-27.8}{14.4} = 4.46$ standard deviations from the mean, which is pretty extreme with n = 1500. Oct 9, 2012 at 13:15
• Im not permitted to post any images, so i post a plot at this adress: space.hgo.se/gis/statistics.jpg Oct 9, 2012 at 13:35
• The trend line is an moving average of 5 Oct 9, 2012 at 13:39
• I would say you do not want to use t-tests here, unless the right tail is of great interest to you. Variables such as size often benefit from a log transformation. Oct 9, 2012 at 13:53