## Using python to create an average out of a list of times

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I have a huge list of times (HH:MM:SS) and I know that if I wanted to create an average I could separate the Hours, Seconds, and Minutes and average each one and then concatenate them back together. However I feel that there must be a better way to do that. Does anyone know of a better way to do this?

Thanks!

You don't want to "average" times on hours, minutes and seconds this way:

00:59:00 01:01:00

average clearly to `01:00:00`

, but not with the logic you presented.

Instead convert all your time intervals into seconds, calculate the average and convert back to `HH:MM:SS`

.

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

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Here is one possible implementation of the answer by @eumiro, but this logic only works if these are durations, not times, as pointed out by @lazyr:

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))))

Also thanks to a post by @SilentGhost, and a post by @Herms

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There's a problem with converting to seconds since midnight and averaging. If you do that with 23:50 and 00:10 you get 12:00 when what you want it 00:00.

A better approach is to average the angles.

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)

**Python statistics,** Pseudo-polynomial Algorithms · Polynomial Time Approximation Scheme mean() function can be used to calculate mean/average of a given list of numbers. It is a measure of the central location of data in a set of values which vary in range. from statistics import mean Check out this Author's contributed articles. First parse the time from string format to time struct using strptime, then convert the time to seconds from epoch using mktime, then you should add all the seconds and divide by the number of times, and to convert back to time struct using localtime

You need to convert it to **complex numbers**, take the argument and then average the degrees.

Finally you'll need to parse date to get what you want and then convert back to the original hour.

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 toAngles = [s * 360. / day for s in seconds] meanAsAngle = meanAngle(toAngles) meanSeconds = meanAsAngle * day / 360. if meanSeconds < 0: meanSeconds += day h, m = divmod(meanSeconds, 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

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First parse the time from string format to time struct using strptime, then convert the time to seconds from epoch using mktime, then you should add all the seconds and divide by the number of times, and to convert back to time struct using localtime

Here is an example:

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)

Note that I added the year 2000 because `mktime`

is giving `OverflowError`

for the default year 1900

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##### Comments

- Give a (short) example of input and output in proper Python.
- how about just taking an absolute time
`total # seconds = hours * 3600 + minutes * 60 + seconds`

and averaging that and putting it back together as a time? - Could you provide some sample data please. Do you have the data in strings, timedelta, etc. ...
- Beware that if what you're averaging is not
*duration*but*points in time*, then it wraps around and the average becomes a wooly concept -- you need to define what happens around midnight. For example, what is the average of`23:59:58`

and`00:00:00`

? Is it`23:59:59`

or`11:59:59`

? - I think this one should have been the accepted answer. It worked perfectly for me. Anyhow, there's one little detail to adjust: the line
`hour = seconds_from_midnight / 3600`

should be modified to`hour = (seconds_from_midnight / 3600) % 24`

to handle cases in which`hour`

has a negative value. The error can be reproduced by computing the mean of, for instance, 18:20 and 20:35 - I think it should be radians = float(seconds_from_midnight) / float(24 * 60 * 60) * 2.0 * math.pi and seconds_from_midnight = int(float(x) / (2.0 * math.pi) * 24.0 * 60.0 * 60.0) note 24 instead of 12 - to make 24 hours = 2pi (360 degrees). And the above comment is still valid.