Add some statistics to the monsoon profile run

tools/telemetry/telemetry/util/statistics.py

 # Copyright 2013 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 """A collection of statistical utility functions to be used by metrics."""
 
 import bisect
 import math
 
 
@@ skipping 141 matching lines @@
 
   Args:
     durations: List of interval lengths in milliseconds.
     absolute: See TimestampsDiscrepancy.
     interval_multiplier: See TimestampsDiscrepancy.
   """
   timestamps = reduce(lambda x, y: x + [x[-1] + y], durations, [0])[1:]
   return TimestampsDiscrepancy(timestamps, absolute, interval_multiplier)
 
 
-def ArithmeticMean(numerator, denominator):
+def ArithmeticMean(data):
   """Calculates arithmetic mean.
 
   Both numerator and denominator can be given as either individual

[tonyg, 2014/03/12 15:28:38]

Nit: update the bit about the denominator.

   values or lists of values which will be summed.
 
   Args:
     numerator: A quantity that represents a sum total value.
     denominator: A quantity that represents a count of the number of things.

[tonyg, 2014/03/12 15:28:38]

Nit: remove this line

 
   Returns:
     The arithmetic mean value, or 0 if the denominator value was 0.
   """
-  numerator_total = Total(numerator)
-  denominator_total = Total(denominator)
+  numerator_total = Total(data)
+  denominator_total = Total(len(data))
   return DivideIfPossibleOrZero(numerator_total, denominator_total)
 
 
+def StandardDeviation(data):

[tonyg, 2014/03/12 15:28:38]

Even though these are really common concepts, I recommend pydoc style comments
like we have in ArithmeticMean().

+  if len(data) == 1:
+    return 0.0
+
+  mean = ArithmeticMean(data)
+  variances = [float(x) - mean for x in data]
+  variances = [x * x for x in variances]
+  std_dev = math.sqrt(ArithmeticMean(variances))
+
+  return std_dev
+
+
+def StandardErrorOfMean(data):
+  if len(data) <= 1:
+    return 0.0
+
+  std_dev = StandardDeviation(data)
+
+  return std_dev / math.sqrt(len(data))
+
+
+def TrapezoidalRule(data, dx):
+  """ Calculate the integral according to trapezoidal rule
+  Approximates the definite integral of f from a to b by
+  the composite trapezoidal rule, using n subintervals
+  http://en.wikipedia.org/wiki/Trapezoidal_rule#Uniform_grid
+  """

[tonyg, 2014/03/12 15:28:38]

The content of this comment is perfect, but please format it according to:
http://google-styleguide.googlecode.com/svn/trunk/pyguide.html#Comments

+  n = len(data) - 1
+  s = data[0] + data[n]
+
+  for i in range(1, n):
+    s += 2 * data[i]
+
+  return s * dx / 2.0
+
 def Total(data):
   """Returns the float value of a number or the sum of a list."""
   if type(data) == float:
     total = data
   elif type(data) == int:
     total = float(data)
   elif type(data) == list:
     total = float(sum(data))
   else:
     raise TypeError
@@ skipping 66 matching lines @@
       new_values.append(value)
     else:
       new_values.append(0.001)
   # Compute the sum of the log of the values.
   log_sum = sum(map(math.log, new_values))
   # Raise e to that sum over the number of values.
   mean = math.pow(math.e, (log_sum / len(new_values)))
   # Return the rounded mean.
   return int(round(mean))