Add some statistics to the monsoon profile run

tools/telemetry/telemetry/util/statistics.py

Index: tools/telemetry/telemetry/util/statistics.py
diff --git a/tools/perf/metrics/statistics.py b/tools/telemetry/telemetry/util/statistics.py
similarity index 87%
rename from tools/perf/metrics/statistics.py
rename to tools/telemetry/telemetry/util/statistics.py
index 84ffc164a333035d2f40a2c2c596b41edc19c126..7044572f0f7b9e7ed202040527c3deb136ea5b71 100644
--- a/tools/perf/metrics/statistics.py
+++ b/tools/telemetry/telemetry/util/statistics.py
@@ -159,24 +159,67 @@ def DurationsDiscrepancy(durations, absolute=True,
   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
-  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.
+    data: A list of samples.
 
   Returns:
-    The arithmetic mean value, or 0 if the denominator value was 0.
+    The arithmetic mean value, or 0 if the list is empty.
   """
-  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):
+  """Calculates the standard deviation.
+
+  Args:
+    data: A list of samples.
+
+  Returns:
+    The standard deviation of the samples provided.
+  """
+  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 TrapezoidalRule(data, dx):
+  """ Calculate the integral according to the trapezoidal rule
+
+  TrapezoidalRule 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
+
+  Args:
+    data: A list of samples
+    dx: The uniform distance along the x axis between any two samples
+
+  Returns:
+    The area under the curve defined by the samples and the uniform distance
+    according to the trapezoidal rule.
+  """
+
+  n = len(data) - 1
+  s = data[0] + data[n]
+
+  if n == 0:
+    return 0.0
+
+  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: