comparing areas under a histogram and its PDF Assumption: we have a histogram, which follows the shape of a normal distribution. The y-axis of this histogram is the relative frequency. The bin size is 5.
My though process(correct me in which step am i wrong):


*

*The area of the histogram then is 5.

*We approximate this histogram into a continuous distribution.

*This continuous distribution is a bell shaped normal distribution which is almost identical to the shape of the histogram.

*This continuous dirstribution is also called the PDF.

*THe area under the continuous distribution is almost equal to the area under the histogram.

*But we know the area under the pdf = 1; however the area under the histogram is 5 


Im getting real confused trying to convert the histogram into a pdf due to this. someone please point out what assumption that i am making is wrong.
 A: Comments:
I think you are confused about the heights and areas of the histogram bars.
Most software packages use a 'density' scale instead of a
'relative frequency' scale so that the total area of all
histogram bars will be unity. 
I don't know the exact terminology of your book and I don't
want to risk adding to the confusion with a direct answer.  
Here is a 'density' histogram from R statistical software of a dataset of size n  = 1000, generated from 
NORM(mean=50, sd=5). Bin widths are 5. What is the area
of each bar? How are densities (heights of bars) computed?
How would the vertical axis be labeled if this were a 'relative frequency histogram'?
Each bar is labeled with its density (slightly rounded). Some information about
the histogram (from a non-plotting version) is also provided.
I hope this is enough hints and information so you can answer
your own question.
 x = rnorm(1000, 50, 5)
 cutpt = seq(20,80,by=5)
 hist(x, prob=T, lab=T, br=cutpt, ylim=c(0, .1), col="skyblue")
 curve(dnorm(x, 50, 5), col="darkgreen", lwd=2, add=T)


 hist(x, prob=T, br=cutpt, plot=F)
 $breaks
  [1] 20 25 30 35 40 45 50 55 60 65 70 75 80

 $counts
  [1]   0   0   1  21 134 336 327 154  25   2   0   0

 $density
  [1] 0.0000 0.0000 0.0002 0.0042 0.0268 0.0672 0.0654 0.0308 0.0050
 [10] 0.0004 0.0000 0.0000


