Standard deviation of a list

Question

I want to find mean and standard deviation of 1st  2nd     digits of several  Z  lists  For example  I have  A rank  0 8 0 4 1 2 3 7 2 6 5 8  B rank  0 1 2 8 3 7 2 6 5 3 4  C Rank  1 2 3 4 0 5 0 1 2 5 6 1    etc  up to Z rank        Now I want to take the mean and std of   Rank 0   the mean and std of   Rank 1   etc   ie  mean and std of the 1st digit from all the  A  Z  rank lists  the mean and std of the 2nd digit from all the  A  Z  rank lists  the mean and std of the 3rd digit     etc

User · Answer

Since Python 3 4   PEP450 there is a statistics module in the standard library  which has a method stdev for calculating the standard deviation of iterables like yours    gt  gt  gt  A rank    0 8  0 4  1 2  3 7  2 6  5 8   gt  gt  gt  import statistics  gt  gt  gt  statistics stdev A rank  2 0634114147853952

User · Answer

In python 2 7 you can use NumPy s numpy std   gives the population standard deviation   In Python 3 4 statistics stdev   returns the sample standard deviation  The pstdv   function is the same as numpy std

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pure python code   from math import sqrt  def stddev lst       mean   float sum lst     len lst      return sqrt float reduce lambda x  y  x   y  map lambda x   x - mean     2  lst      len lst

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In Python 2 7 1  you may calculate standard deviation using numpy std   for    Population std  Just use numpy std   with no additional arguments besides to your data list  Sample std  You need to pass ddof  i e  Delta Degrees of Freedom  set to 1  as in the following example        numpy std  lt  your-list    ddof 1        The divisor used in calculations is N - ddof  where N represents the number of elements  By default ddof is zero    It calculates sample std rather than population std

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The other answers cover how to do std dev in python sufficiently  but no one explains how to do the bizarre traversal you ve described   I m going to assume A-Z is the entire population  If not see Ome s answer on how to inference from a sample   So to get the standard deviation mean of the first digit of every list you would need something like this    standard deviation numpy std  A rank 0   B rank 0   C rank 0        Z rank 0      mean numpy mean  A rank 0   B rank 0   C rank 0        Z rank 0      To shorten the code and generalize this to any nth digit use the following function I generated for you   def getAllNthRanks n       return  A rank n   B rank n   C rank n   D rank n   E rank n   F rank n   G rank n   H rank n   I rank n   J rank n   K rank n   L rank n   M rank n   N rank n   O rank n   P rank n   Q rank n   R rank n   S rank n   T rank n   U rank n   V rank n   W rank n   X rank n   Y rank n   Z rank n      Now you can simply get the stdd and mean of all the nth places from A-Z like this    standard deviation numpy std getAllNthRanks n     mean numpy mean getAllNthRanks n

User · Answer

Here s some pure-Python code you can use to calculate the mean and standard deviation   All code below is based on the statistics module in Python 3 4    def mean data          Return the sample arithmetic mean of data         n   len data      if n  lt  1          raise ValueError  mean requires at least one data point       return sum data  n   in Python 2 use sum data  float n   def  ss data          Return sum of square deviations of sequence data         c   mean data      ss   sum  x-c   2 for x in data      return ss  def stddev data  ddof 0          Calculates the population standard deviation     by default  specify ddof 1 to compute the sample     standard deviation         n   len data      if n  lt  2          raise ValueError  variance requires at least two data points       ss    ss data      pvar   ss  n-ddof      return pvar  0 5   Note  for improved accuracy when summing floats  the statistics module uses a custom function  sum rather than the built-in sum which I ve used in its place   Now we have for example    gt  gt  gt  mean  1  2  3   2 0  gt  gt  gt  stddev  1  2  3     population standard deviation 0 816496580927726  gt  gt  gt  stddev  1  2  3   ddof 1    sample standard deviation 0 1

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Using python  here are few methods   import statistics as st  n   int input    data   list map int  input   split       Approach1 - using a function  stdev   st pstdev data    Approach2  calculate variance and take square root of it  variance   st pvariance data  devia   math sqrt variance    Approach3  using basic math  mean   sum data  n variance   sum    x - mean     2  for x in X     n stddev   variance    0 5  print   0 0 1f   format stddev     Note    variance calculates variance of sample population  pvariance calculates variance of entire population  similar differences between stdev and pstdev

User · Answer

I would put A Rank et al into a 2D NumPy array  and then use numpy mean   and numpy std   to compute the means and the standard deviations   In  17   import numpy  In  18   arr   numpy array  A rank  B rank  C rank    In  20   numpy mean arr  axis 0  Out 20    array   0 7          2 2          1 8          2 13333333   3 36666667          5 1           In  21   numpy std arr  axis 0  Out 21    array   0 45460606   1 29614814   1 37355985   1 50628314   1 15566239          1 2083046

[python] Standard deviation of a list

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