# Calculating variance and standard deviation of continuous time series

I am trying to calculate the variance and standard deviation of an unevenly spaced continuous time series. Example data:

Time    Value
0       0
1000    1
2000    2
3000    3
5000    4


Where Time is the duration since the start of the time series. Duration between points is not guaranteed to be uniform.

Values are continuous, e.g. the temperature measured throughout a day.

The arithmetic mean is weighted by Time, resulting in a mean for this example data being 2.3

How do I calculate the variance and standard deviation of Value in a continuous unevenly spaced time series?