Visualise and interpret large set of univariate skewed data I am trying to find out answer for this simple question. I have data (list of numbers). I have  20000 numbers. smallest number is 100 and largest is 15000. I want to interpret this data, how it is distributed or any other suggestions, that how can I play with this data and do different things?
The thing is I have to give a presentation on summary stats on this data and also I want to include plots of this data in my presentation so that I can easily show to everyone, what data looks like, to tell them, which is largest number, smallest, which range of numbers are occurring more. 
So I have made histogram in R but for so many numbers, histogram is not a good choice. Also I know how to calculate all this mean, median and standard deviation. This is not a homework, I want to give presentation about the data, and I am not a statistician.
 A: A lot of the expenditure data I work with has a similar distribution to this.  Depending on what you need to do we often find it useful to plot a histogram of the logarithm of the data.  This can be done by transforming the variable and plotting that, or plotting the original data on a logarithmic axis.
This method can be useful for having another think about your outliers - are they really exceptional cases, or are they just the natural high values you'd expect with what an underlying distribution that is quite regular eg approximately log normal.
For most audiences, it would be a good idea to present the original as well, as otherwise they can easily otherwise walk away with the incorrect idea that your data is symmetrically distributed when it is far from it.
Then, a quantile-quantile plot is the best way of comparing the distribution of your variable to some reference distribution.  A qq-plot comparing the log of our "spend" variable compared to a normal distribution is included below.  This shows that our distribution isn't actually log-normal, but for a reasonable amount of its range, including the higher values, it is a reasonable approximation.  Interpreting qq-plots needs a bit of practice but there are plenty of explanations out there.
eg
library(ggplot2)
qplot(TotalSpend) # this is just a histogram
qplot(TotalSpend, log="x")
qplot(sample=log(TotalSpend), stat="qq") # or qqnorm() if you prefer


A: A histogram is a fine choice when you have lots of data.  I'm guessing your problems are that with a histogram:


*

*your high outliers won't be noticed.

*the visual is too small because the x-axis is stretched long enough to capture the high outliers.
Solve problem 1 with a note below the graph: "There are large outliers which are not visible."  
Solve problem 2 by reducing the range, something like: hist(x, xlim=range(0:2000))
@chl pointed out that my description was a bit unclear so I've edited it lightly.  He/she also points out that you'll probably need to adjust other parameters to make a good looking histogram, e.g. "breaks" which affects bin size.  Of course there are other packages you could use for your plotting.  lattice and ggplot2 are two popular alternatives to the base R graphics.
In addition to calculating the standard deviation, you might use a function like describe from package Hmisc.  It provides output like this:
ih$bweightoz : birthweight in ounces 
      n missing  unique    Mean     .05     .10     .25     .50 
  16548    4197     136   115.4    75.0    86.7   103.0   117.0 
    .75     .90     .95 
  129.0   142.0   151.0 

lowest :  48.01  64.00  64.01  65.00  66.00
highest: 187.00 188.00 190.00 191.00 192.01 

A: A histogram would do exactly that. For descriptive stats, the mean, standard deviation and skewness, as well as the IQR are the most commonly used. Depending on the type of distribution, some of those become more or less relevant -- a mean isn't really representative in a highly skewed distribution, for instance. You would probably prefer the median, which is less sensitive to extremes.
A: A box plot shows the summary statistics. Try a box plot. 
