Togaware DATA MINING
Desktop Survival Guide
by Graham Williams
Google

Textual Summaries

The summary function provides the first insight into how the values for each variable are distributed:

> summary(wine)

 Type      Alcohol          Malic            Ash          Alcalinity   
 1:59   Min.   :11.03   Min.   :0.740   Min.   :1.360   Min.   :10.60  
 2:71   1st Qu.:12.36   1st Qu.:1.603   1st Qu.:2.210   1st Qu.:17.20  
 3:48   Median :13.05   Median :1.865   Median :2.360   Median :19.50  
        Mean   :13.00   Mean   :2.336   Mean   :2.367   Mean   :19.49  
        3rd Qu.:13.68   3rd Qu.:3.083   3rd Qu.:2.558   3rd Qu.:21.50  
        Max.   :14.83   Max.   :5.800   Max.   :3.230   Max.   :30.00  

   Magnesium         Phenols        Flavanoids    Nonflavanoids   
 Min.   : 70.00   Min.   :0.980   Min.   :0.340   Min.   :0.1300  
 1st Qu.: 88.00   1st Qu.:1.742   1st Qu.:1.205   1st Qu.:0.2700  
 Median : 98.00   Median :2.355   Median :2.135   Median :0.3400  
 Mean   : 99.74   Mean   :2.295   Mean   :2.029   Mean   :0.3619  
 3rd Qu.:107.00   3rd Qu.:2.800   3rd Qu.:2.875   3rd Qu.:0.4375  
 Max.   :162.00   Max.   :3.880   Max.   :5.080   Max.   :0.6600  

 Proanthocyanins     Color             Hue            Dilution    
 Min.   :0.410   Min.   : 1.280   Min.   :0.4800   Min.   :1.270  
 1st Qu.:1.250   1st Qu.: 3.220   1st Qu.:0.7825   1st Qu.:1.938  
 Median :1.555   Median : 4.690   Median :0.9650   Median :2.780  
 Mean   :1.591   Mean   : 5.058   Mean   :0.9574   Mean   :2.612  
 3rd Qu.:1.950   3rd Qu.: 6.200   3rd Qu.:1.1200   3rd Qu.:3.170  
 Max.   :3.580   Max.   :13.000   Max.   :1.7100   Max.   :4.000  

    Proline      
 Min.   : 278.0  
 1st Qu.: 500.5  
 Median : 673.5  
 Mean   : 746.9  
 3rd Qu.: 985.0  
 Max.   :1680.0

Next, we would like to know how the data is distributed. For categoric variables this will be how many of each level there are. For numeric variables this will be the mean and median, the minimum and maximum values, and an idea of the spread of the values of the variable.

We would also like to know about missing values (referred to in R as NAs--short for Not Available), and the summary function will also report this:



> load("survey.RData")
> summary(survey)
[...]
       Native.Country  Salary.Group
 United-States:29170   <=50K:24720
 Mexico       :  643   >50K : 7841
 Philippines  :  198
 Germany      :  137
 Canada       :  121
 (Other)      : 1709
 NA's         :  583

We also see here that the categoric variable Native.Country has more than five levels, and there are 1,709 entities with values for this variable other than the five listed here. The five listed are the most frequently occurring.

The mean provides a measure of the average or central tendency of the data. It is denoted as $\mu$ if $x_1,\ldots,x_n$ is the whole population (population mean), and $\overline{X}$ if it is a sample of the population (sample mean).

In calculating the mean of a sample from a population we generally need at least 30 observations in the sample before it makes sense. This is based on the central limit theorem that indicates that for $n=30$ the shape of a distribution approaches normal.

R provides the mean function to calculate the mean. The mean is also reported as part of the output from summary. The summary function in fact will use the method associated with the data type of the object passed. For example, if it is a data frame the function summary.data.frame will be called upon. To see the actual function definition, simply type the function name at the command line (without brackets). The actual code will be printed out. A user can then fine tune the function, if desired.

A quick trick to roughly get the mode of a dataset is to use the denisity.



mode <- function (n)
{
  n <- as.numeric(n)    
  n.density <- density(n)
  round(n.density$x[which(n.density$y==max(n.density$y))])
}

You can then simply write your own functions to summarise the data using sapply:

> sapply(wine, 
         function(x) 
         {
           x <- as.numeric(x)
           res <- c(mean(x), median(x), mode(x), mad(x), sd(x))
           names(res) <- c("mean", "median", "mode", "mad", "sd")
           res
         })

          Type    Alcohol    Malic      Ash Alcalinity Magnesium  Phenols
mean   1.938202 13.0006180 2.336348 2.366517  19.494944  99.74157 2.295112
median 2.000000 13.0500000 1.865000 2.360000  19.500000  98.00000 2.355000
mode   2.000000 14.0000000 2.000000 2.000000  19.000000  90.00000 3.000000
mad    1.482600  1.0081680 0.770952 0.237216   3.039330  14.82600 0.748713
sd     0.775035  0.8118265 1.117146 0.274344   3.339564  14.28248 0.625851

       Flavanoids Nonflavanoids Proanthocyanins    Color       Hue  Dilution
mean    2.0292697     0.3618539       1.5908989 5.058090 0.9574494 2.6116854
median  2.1350000     0.3400000       1.5550000 4.690000 0.9650000 2.7800000
mode    3.0000000     0.0000000       1.0000000 3.000000 1.0000000 3.0000000
mad     1.2379710     0.1260210       0.5633880 2.238726 0.2446290 0.7709520
sd      0.9988587     0.1244533       0.5723589 2.318286 0.2285716 0.7099904

        Proline
mean   746.8933
median 673.5000
mode   553.0000
mad    300.2265
sd     314.9075

In the following sections we provide graphic presentations of the mean and standard variation.

Copyright © 2004-2010 Togaware Pty Ltd
Support further development through the purchase of the PDF version of the book.
The PDF version is a formatted comprehensive draft book (with over 800 pages).
Brought to you by Togaware. This page generated: Sunday, 22 August 2010