I plotted a histogram below that is the mean density of multiple vectors. The frequency distribution of each vector is shown by the grey lines overlaid on the histogram. Rather than plotting each of these lines, is there a way to plot the standard deviation above and below the mean for the frequency distribution across the vectors? That is, the standard deviation of the grey lines.

I tried getting the density of each vector and calculating the standard deviation of the y variable, but the line from that did not seem to correspond to the mean.

```
ln <- length(names(data))
hist(data_mean, breaks=100, prob=TRUE)
for( i in 1:ln ) {
lines(density(data[,i], na.rm = TRUE), col="grey", lwd=1)
}
dev.off()
```

Answer:

I think the code below will work. In short, I determine the densities of each vector, approx to some known vector of x values, jam it all together in a matrix, and then calculate the summary stats and plot. Is this what you were looking to do?

```
#Make up some fake data (each column is a sample)
mat=matrix(rnorm(5000,2,0.5),ncol=50)
#Determine density of each column
dens=apply(mat, 2, density)
#Interpolate the densities so they all have same x coords
approxDens=lapply(dens, approx, xout=seq(0.1,3.5,by=0.1))
#Create your output matrix, and fill it with values
approxDens2=matrix(0, ncol=ncol(mat), nrow=length(approxDens[[1]]$y))
for(i in 1:length(approxDens)){
approxDens2[,i]=approxDens[[i]]$y}
#Determine the mean and sd of density values given an x value
mn = rowMeans(approxDens2)
stdv = apply(approxDens2,1,sd)
#pull out those x values you approx-ed things by for plotting
xx = approxDens[[1]]$x
#plot it out
plot(xx, mn, las=1, ylim=c(0,1), type='l', ylab='Density', xlab='X')
lines(xx, mn+stdv, lty=2);lines(xx, mn-stdv, lty=2)
```

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