mean, median and mode

this page explains a mean minimizes the  norm of the residual: 
a median minimizes its  norm and a mode minimizes the zero norm of the residual, namely .See the wikipedia page about median.

from here, it was further explained that

Inder Jeet Taneja’s book draft has a nice survey of the results: if you fix the upper and lower boundary, and maximize entropy, you’ll get the uniform distribution. If you fix the mean and the expected L2 norm (d^2) between the mean and the distribution, maximizing the entropy you’ll get the Gaussian. If you fix the expected L1 norm (|d|) between the mean and the distribution, maximizing the entropy you’ll get the Laplace (also referred to as Double Exponential). Moreover, log(1+d^2) norm will yield the Cauchy distribution – a special case of the standard heavy-tailed Student distribution.

check points when reviewing a genetic screening report

1. title and footnote, ensuring it describes the analysis population, the outcome variable and the class of genetic markers; 
2. eyeball examples:
• 1 example of x chr snp
• 1 example of autosomal snp with only 2 genotypes
• 1 example of top association 
• 1 example of a random association
3. use the excel output to check the value ranges for each column, pay attention to
• extreme values
• empty cells
• characters indicating missing: -,NA, 0
4. Cosmetic issues
• decimal places
• check line ends for character cut off