Hi Guys

Could you please help me to determine if this histogram looks normal or not?

Thanks

It would help to see the original data and/or how the analysis was done. But here are a couple observations:



The general "bell curve" part "looks normal (but judging such things by eye can be deceiving) . It appears that the curve plotted is a normal distribution with a mean of 49.4865 and a st dev of 1.24. The two follow each other pretty well for the most part.
On the other hand, there are a few extreme outliers. The highest data point is over 10 standard deviations above the mean, which would be way less than 1 in a trillion odds.
I'm no sure what the "SW-W" means at the bottom, but I am guessing that the next "p=0.0000" is the odds that this distribution fits a normal distribution. In other words, the statistical test rules out this being from a normal distribution. But that is just a guess as to what this p value refers to.


My "hunch" is that if you removed the outliers this would be close enough to a normal distribution for any practical purposes. With those few extreme outliers, then you have some significant deviations from a normal distribution.


Tim F

I always think it is useful to see the run chart that goes along with the histogram to see how it tracks along the samples. Multiple populations can easily overlap and make a histogram look better than it is. Also the sample goes into play (is it a 2 off die, casting with multiple cavities, multiple molds, multiple machines running the same part etc). The specs also help in the determination. The couple outliers become more minor if the spec is zero to 100 than say +/- 5.

Sometime you don’t want a centered process but still a tight distribution. Example is drilling or stamping. The wear on the perishable tools are only going to go one direction. Why lose half your tool life starting at nominal? The important thing is to understand and make a conscious decision for it. Two suppliers had similar charts (shifted high) and when asked one says the above (trust him that he is looking at his data and running the process and monitoring tool wear) vs the other who says don’t know that’s what I got (watch out that his process is running him and he’s letting not working to monitor it). Same results but only one for the right reason.

I will second what Jaxqc said about looking at the run chart. That said, my almost immediate reaction to a chart that looks like this is that you have a normal distribution (which implies nothing but random variation) with a few outliers that have some assignable causes, aka non-random variation. If you can look at the outliers, and say "This point is out of the normal distribution because X happened here and not elsewhere." then you have a normal population.

Geoff Withnell

An alternative response that might provide better answers to th eOP is to ask him why he asking? the histogram was obviously created with statistical software - doesnt' it have a Normality test? then why does it matter if the distribution is Normal? we might provide very different and ultimately more helpful answers if knew the intended purpose...There is no practical reason for simply knowing if a distribution is Normal...