R help - Mar 2008 - hist densities

Hi there,

I was wondering why

x<-rnorm(n=5000,mean=1.5,sd=0.25)
h<-hist(x)
sum(h$density)

[1] 10

I thought the integral of the histogram should be one? These seems  
strange to me, or am I being silly...

Regards Luke Spadavecchia

PS. I'm using R 2.5.1 on Mac OSX

On Fri, 21 Mar 2008, Luke Spadavecchia wrote:
> Hi there,
>
> I was wondering why
>
> x<-rnorm(n=5000,mean=1.5,sd=0.25)
> h<-hist(x)
> sum(h$density)
>
> [1] 10
>
> I thought the integral of the histogram should be one? These seems
> strange to me, or am I being silly...
The integral is not a sum of heights but of areas.  You need
sum(h$density * diff(h$breaks)), and this is spelled out on the help page.
> Regards Luke Spadavecchia
>
> PS. I'm using R 2.5.1 on Mac OSX
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
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