title: calculate centroid of pandas series
body: <p>I've got a pandas series with a datetime index (eg. precipitation). I would like to calculate the centroid of this precipitation time series (the mean of the datetime weighted by the value). My problem is that I cannot multiply a datetime object with a float. The (not working) idea looks like this (output should be a datetime object):</p>
  
  <pre><code>import pandas as pd
  import datetime as dt
  df = pd.DataFrame({'P':[1.2,10.1,5.6,0,0,0,0,0,3,4,6,4,8,2,0,0,0,0,0,0,0,0,0,0]}, index=[dt.datetime(2012,1,1,h) for h in range(24)])
  P_sum = df['P'].sum()
  prod = df.index * df['P']/P_sum
  mean_date = prod.mean()
  </code></pre>