簡單統計

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除了 `mode` 以外的所有函數都會跳過所有非數字資料，而且表格無須建立索引。例如

t = {[1]=5, [2]=7, [3]=8, [4]='Something else.'}  -- or
t = {["a"]=5, ["b"]=7, ["c"]=8, ["name"]='My table of numbers'}

適合做為這些函數的輸入。請注意，「眾數」函數略有不同。它可以處理任何資料，而不僅限於數字。

-- Small stats library                      --
----------------------------------------------
-- Version History --
-- 1.0 First written.

-- Tables supplied as arguments are not changed.


-- Table to hold statistical functions
stats={}

-- Get the mean value of a table
function stats.mean( t )
  local sum = 0
  local count= 0

  for k,v in pairs(t) do
    if type(v) == 'number' then
      sum = sum + v
      count = count + 1
    end
  end

  return (sum / count)
end

-- Get the mode of a table.  Returns a table of values.
-- Works on anything (not just numbers).
function stats.mode( t )
  local counts={}

  for k, v in pairs( t ) do
    if counts[v] == nil then
      counts[v] = 1
    else
      counts[v] = counts[v] + 1
    end
  end

  local biggestCount = 0

  for k, v  in pairs( counts ) do
    if v > biggestCount then
      biggestCount = v
    end
  end

  local temp={}

  for k,v in pairs( counts ) do
    if v == biggestCount then
      table.insert( temp, k )
    end
  end

  return temp
end

-- Get the median of a table.
function stats.median( t )
  local temp={}

  -- deep copy table so that when we sort it, the original is unchanged
  -- also weed out any non numbers
  for k,v in pairs(t) do
    if type(v) == 'number' then
      table.insert( temp, v )
    end
  end

  table.sort( temp )

  -- If we have an even number of table elements or odd.
  if math.fmod(#temp,2) == 0 then
    -- return mean value of middle two elements
    return ( temp[#temp/2] + temp[(#temp/2)+1] ) / 2
  else
    -- return middle element
    return temp[math.ceil(#temp/2)]
  end
end
    

-- Get the standard deviation of a table
function stats.standardDeviation( t )
  local m
  local vm
  local sum = 0
  local count = 0
  local result

  m = stats.mean( t )

  for k,v in pairs(t) do
    if type(v) == 'number' then
      vm = v - m
      sum = sum + (vm * vm)
      count = count + 1
    end
  end

  result = math.sqrt(sum / (count-1))

  return result
end

-- Get the max and min for a table
function stats.maxmin( t )
  local max = -math.huge
  local min = math.huge

  for k,v in pairs( t ) do
    if type(v) == 'number' then
      max = math.max( max, v )
      min = math.min( min, v )
    end
  end

  return max, min
end