# Calculate an incremental mean using python pandas

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I’d like to generate a series that’s the incremental mean of a timeseries. Meaning that, starting from the first date (index 0), the mean stored in row x is the average of values [0:x]

``````data
index   value   mean          formula
0       4
1       5
2       6
3       7       5.5           average(0-3)
4       4       5.2           average(0-4)
5       5       5.166666667   average(0-5)
6       6       5.285714286   average(0-6)
7       7       5.5           average(0-7)
``````

I’m hoping there’s a way to do this without looping to take advantage of pandas.

Here’s an update for newer versions of Pandas (starting with 0.18.0)

``````df['value'].expanding().mean()
``````

or

``````s.expanding().mean()
``````

As @TomAugspurger points out, you can use `expanding_mean`:

``````In : s = pd.Series([4, 5, 6, 7, 4, 5, 6, 7])

In : pd.expanding_mean(s, 4)
Out:
0         NaN
1         NaN
2         NaN
3    5.500000
4    5.200000
5    5.166667
6    5.285714
7    5.500000
dtype: float64
``````

Another approach is to use cumsum(), and divide by the cumulative number of items, for example:

``````In :
s = pd.Series([4, 5, 6, 7, 4, 5, 6, 7])
s.cumsum() / pd.Series(np.arange(1, len(s)+1), s.index)

Out:
0    4.000000
1    4.500000
2    5.000000
3    5.500000
4    5.200000
5    5.166667
6    5.285714
7    5.500000
dtype: float64
`````` The answers/resolutions are collected from stackoverflow, are licensed under cc by-sa 2.5 , cc by-sa 3.0 and cc by-sa 4.0 .