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is this histogram normally distributed

Is this histogram normally distributed? I can't tell since there are peaks that are outside the curve.

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    $\begingroup$ What are the data? $\endgroup$ – gung - Reinstate Monica May 18 '16 at 10:51
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    $\begingroup$ I guess your software has added a normal density curve with the same mean and standard deviation as the data. If not, tell us how the histogram was produced. The fit would be perfect if the bar tops (peaks in your wording) matched the curve. If some bars lie above the curve, it's inevitable that some also lie below. What wording people use depends partly on how strong the expectation is that the distribution will be normal, but the fit certainly isn't perfect or even good: I would say that the fit is at best moderate, but whether this matters depends on what you want to do next. . $\endgroup$ – Nick Cox May 18 '16 at 11:01
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    $\begingroup$ "I can't tell" is a puzzling comment as the graph is directly informative about the fit to a normal. $\endgroup$ – Nick Cox May 18 '16 at 11:02
  • $\begingroup$ Probably not - high peak, and some right skewness as well $\endgroup$ – probabilityislogic May 18 '16 at 11:09
  • $\begingroup$ We can't tell as you say nothing about context here, but often when people look at differences, there's an expectation that their mean is zero. So, if the reference distribution is a normal with mean zero, then the fit is even poorer than implied. $\endgroup$ – Nick Cox May 18 '16 at 11:34
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I'll try to re-phrase the already comprehensive answer by Nick Cox: Your (yellow-ish) data histogram is compared in the plot to a normal distribution of the same first two moments (expectation and variance), drawn in black. It is entirely expected that some bars of the histogram are above that line and some are below (by the very definition of a histogram). Thus, gung's reply "What are the data?" is warranted ;-)

Note that the answer to your question depends on the metric you want to apply. To put numbers to it, you may try and fit a gaussian distribution manually and look at the Chi^2 yourself. Interpretation must be done by the field expert (which is you)

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As a supplement to the above answers:

At first approximation we can say that the distribution is normal. The Q-Q plots are another way to check the assumption of normality.

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