9.1.4 The population standard deviation: stddevp stdDev
Given a large population, rather than collecting all of the numbers it
might be more feasible to get a smaller collection of numbers and try
to extrapolate from that. For example, to get information about the
ages of a large population, you might get the ages of a sample of 100
of the people and work with that.
If a list of numbers is a sample of data from a larger population,
then the mean of the sample
can be used to estimate the mean of the population. The
standard deviation uses the mean to find the standard deviation of the
sample, but since the mean of the sample is only an approximation to
the mean of the entire population, the standard deviation of the
sample doesn’t provide an optimal estimate of the standard deviation
of the population. An unbiased estimate of the standard deviation of
the entire population is given by the population standard deviation;
given a list L = [x1,…,xn] with
mean µ, the population standard deviation is
| s =
| | |
| (x1 − µ)2 + … + (xn − µ)2 |
|
| n−1 |
|
| .
|
Note that
where σ is the standard deviation of the sample.
The stddevp command finds the standard deviation.
stdDev is a synonym for stddevp, for TI
compatibility. There is no population variance function; if needed,
it can be computed by squaring the stddevp function.
-
stddevp takes one mandatory argument and one optional
argument:
-
L, a list or matrix of numbers.
- W, a list or matrix of weights, the same size as L.
- stddevp(L ⟩ W⟨) returns the population
standard deviation of the list or a list with the population
standard deviations of the columns of the matrix.
Examples.
-
Input:
stddev([1,2,3,4])
Output:
while:
Input:
stddevp([1,2,3,4])
Output:
- Input:
| A:= [0,1,2,3,4,5,6,7,8,9,10,11]
stddevp(A,A)
|
Output: