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Basic statistics

Population

• Mean is designated by μ (lower case mu)
• Standard error (SE) is designated by σ because it is a standard deviation. σ is rarely known and so is estimated from a sample by either:
  • The standard deviation of its sampling distribution: σ_M / sqrt (N)
  • The variance of the sampling distribution: σ²_M/N
• Variance is σ²

Samples

• μ_M = μ
• Standard deviation is designated by σ_M (lower case Greek sigma or the Latin letter s) and is:
  • σ_M = σ / sqrt (N) and so is smaller than the σ of the population
• Variance, σ_M is:
  • σ_M²
  • σ²/N and so is smaller than the σ² of the population

See example at https://en.wikipedia.org/wiki/Variance#/media/File:Comparison_standard_deviations.svg From WikiPedia and http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html

Human performance

From:

Bock, Laszlo. Work Rules!: Insights from Inside Google That Will Transform How You Live and Lead. Grand Central Publishing. Kindle Edition.

Bock writes:

• "human performance in organizations follows a power law distribution for most jobs. Herman Aguinis and Ernest O’Boyle of Indiana University and the University of Iowa explain that “instead of a massive group of average performers dominating… through sheer numbers, a small group of elite performers [dominate] through massive performance.”
• "Individual performance also follows a power law distribution. In many fields it’s easy to point to people whose performance surpasses their peers’ by an inhuman amount."
• "Of course, this doesn’t apply everywhere. As O’Boyle and Aguinis point out, “Industries and organizations that rely on manual labor, have limited technology, and place strict standards for both minimum and maximum production” are places where you’ll see a normal distribution of performance. In those environments there’s little opportunity for exceptional achievement. But everywhere else, this distribution holds sway."

Bock cites:

1. Ernest O’Boyle Jr. and Herman Aguinis, “The Best and the Rest: Revisiting the Norm of Normality of Individual Performance,” Personnel Psychology 65, no. 1 (2012): 79–119. http://doi.org/10.1111/j.1744-6570.2011.01239.x
2. Herman Aguinis and Ernest O’Boyle Jr., “Star Performers in Twenty-First Century Organizations” Personnel Psychology 67, no. 2 (2014): 313–350. https://doi.org/10.1111/peps.12054