00:59:00
01:01:00

00:59:00 -> 3540 seconds
01:01:00 -> 3660 seconds
            ============
average:    3600 seconds converted to HH:MM:SS -> 01:00:00

from datetime import timedelta

times = ['00:58:00','00:59:00','01:00:00','01:01:00','01:02:00']

print(str(timedelta(seconds=sum(map(lambda f: int(f[0])*3600 + int(f[1])*60 + int(f[2]), map(lambda f: f.split(':'), times)))/len(times))))

import time


a = time.strptime("2000:11:12:13","%Y:%H:%M:%S")
b = time.strptime("2000:11:14:13","%Y:%H:%M:%S")

avg_time = time.localtime(((time.mktime(a)+time.mktime(b))/2))

>> time.struct_time(tm_year=2000, tm_mon=1, tm_mday=1, tm_hour=11, tm_min=13, tm_sec=13, tm_wday=5, tm_yday=1, tm_isdst=0)

import datetime
import math
import numpy

def datetime_to_radians(x):
    # radians are calculated using a 24-hour circle, not 12-hour, starting at north and moving clockwise
    time_of_day = x.time()
    seconds_from_midnight = 3600 * time_of_day.hour + 60 * time_of_day.minute + time_of_day.second
    radians = float(seconds_from_midnight) / float(12 * 60 * 60) * 2.0 * math.pi
    return radians

def average_angle(angles):
    # angles measured in radians
    x_sum = numpy.sum([math.sin(x) for x in angles])
    y_sum = numpy.sum([math.cos(x) for x in angles])
    x_mean = x_sum / float(len(angles))
    y_mean = y_sum / float(len(angles))
    return numpy.arctan2(x_mean, y_mean)

def radians_to_time_of_day(x):
    # radians are measured clockwise from north and represent time in a 24-hour circle
    seconds_from_midnight = int(float(x) / (2.0 * math.pi) * 12.0 * 60.0 * 60.0)
    hour = seconds_from_midnight / 3600
    minute = (seconds_from_midnight % 3600) / 60
    second = seconds_from_midnight % 60
    return datetime.time(hour, minute, second)

def average_times_of_day(x):
    # input datetime.datetime array and output datetime.time value
    angles = [datetime_to_radians(y) for y in x]
    avg_angle = average_angle(angles)
    return radians_to_time_of_day(avg_angle)

average_times_of_day([datetime.datetime(2017, 6, 9, 0, 10), datetime.datetime(2017, 6, 9, 0, 20)])
# datetime.time(0, 15)

average_times_of_day([datetime.datetime(2017, 6, 9, 23, 50), datetime.datetime(2017, 6, 9, 0, 10)])
# datetime.time(0, 0)

time_list = map(lambda s: int(s[6:8]) + 60*(int(s[3:5]) + 60*int(s[0:2])), mylist)
 average = sum(time_list)/len(time_list)
 bigmins, secs = divmod(average, 60)
 hours, mins = divmod(bigmins, 60)
 print "%02d:%02d:%02d" % (hours, mins, secs)

from cmath import rect, phase
from math import radians, degrees

def meanAngle(deg):
    complexDegree = sum(rect(1, radians(d)) for d in deg) / len(deg)
    argument = phase(complexDegree)
    meanAngle = degrees(argument)
    return meanAngle

def meanTime(times):
    t = (time.split(':') for time in times)
    seconds = ((float(s) + int(m) * 60 + int(h) * 3600)
               for h, m, s in t)
    day = 24 * 60 * 60
    to_angles = [s * 360. / day for s in seconds]
    mean_as_angle = mean_angle(to_angles)
    mean_seconds = mean_as_angle * day / 360.
    if mean_seconds < 0:
        mean_seconds += day
    h, m = divmod(mean_seconds, 3600)
    m, s = divmod(m, 60)
    return '%02i:%02i:%02i' % (h, m, s)


print(meanTime(["15:00:00", "21:00:00"]))
# 18:00:00
print(meanTime(["23:00:00", "01:00:00"]))
# 00:00:00