Statistics Toolbox

Percentiles

Another option is to compute a reasonable number of the sample percentiles. This provides information about the shape of the data as well as its location and spread.

The example shows the result of looking at every quartile of a sample containing a mixture of two distributions.

• x = [normrnd(4,1,1,100) normrnd(6,0.5,1,200)];
  p = 100*(0:0.25:1);
  y = prctile(x,p);
  z = [p;y]
  z =
           0   25.0000   50.0000   75.0000  100.0000
      1.5172    4.6842    5.6706    6.1804    7.6035
  

Compare the first two quantiles to the rest.

The box plot is a graph for descriptive statistics. The graph below is a box plot of the data above.

• boxplot(x)
  
  
  
  
  

The long lower tail and plus signs show the lack of symmetry in the sample values. For more information on box plots, see Statistical Plots.

The histogram is a complementary graph.

• hist(x)
  
  
  

Percentiles and Graphical Descriptions

Probability Density Estimation