How to calculate divergence from standard deviation I have 20 people I wish to give performance score every 6 months. I want to identify the weakest performers in the bottom 10 and remove them from the group but only those from the point of the most significant drop in performance. I am willing to accept there may well be a perfectly linear decline in score with no sudden drop however my thinking is that by obtaining the standard deviation amongst the top 10 I can identify the greatest precipice drop amongst the bottom ten.
Is standard deviation the correct term to use and how would I go about calculating this ? 
 A: Comment: I have a problem grasping the usefulness of a criterion based on
the maximum gap. 
Perhaps the usual distribution of scores would have something like the following density function with support $(0,100),$ based on a multiple of
the distribution $\mathsf{Beta}(8,2)$ with mean $\mu = 80$ and median $\eta = 82.$
curve(.01*dbeta(.01*x, 8, 2), 0, 100, lwd=2, col="blue", ylab="PDF",
    main="Density of 100*BETA(8,2)")
  abline(h=0, col="green3");  abline(v=c(0,100), col="green3")


Then one can simulate the size of the average gap (which will usually lie among
the lower values) among $n = 20$ observations from this distribution.
In the average 6-month scoring, there will be a maximum gap of about 11,
and about 52% of the time there will be a largest gap of at least 9.
md = replicate(10^5, max(diff(sort(rbeta(20,8,2)*100))) )
mean(md)
[1] 10.66218
mean(md > 9)
[1] 0.51689


Thus it seems that a fairly normal state of affairs would be to fire
employees. Obviously, 10 of 20 employees will be in the lower half (below about 82) at
each scoring, and about half of the time some will happen to be below
a sizable gap.
If your actual distribution is skewed in this way, I don't see how the
sample standard deviation will help you pick the employees below a 'significant'
gap.
Addendum. To give an idea how boxplot outliers would work, here are boxplots for 15 groups of 20 employees each. I assume the same beta-based distribution as above. A common outlier criterion is that an 'outlier' is a value less than 1.5(IQR) below $Q_1$ or more than 1.5(IQR) above $Q_3,$ where $Q_1, Q_3$ are the lower and upper sample quartiles and IQR = $Q_3-Q_1.$ As an experiment, I altered this rule to
be somewhat more aggressive in designating outliers, using IQR instead of 1.5(IQR), that is controlled by the range parameter in R's boxplot function. Because of
the skewness of the population distribution high outliers are extremely rare.
# Code for top panel
set.seed(2011);  gp = as.factor(rep(1:15, each=20));  n = 20
x = 100*rbeta(300, 8, 2)
boxplot(x ~ gp, range=1, col="skyblue2", pch=20)


(Top) About half of the 15 boxplots show at least one outlier. Different runs with different simulated data according to the same distribution (different set.seed statement) had as many as 10 groups with outliers. (Bottom) With the same data,
only three groups showed outliers (one outlier in each group), according to the 1.5(IQR) criterion.
