Interpolate daily values from monthly averages I have a list of monthly production guarantees and I want to estimate daily values. Dividing monthly totals by days/month works, but when graphed, leads to a chunky piece-wise plot. I could use a spline interpolation, but this would not guarantee that the monthly totals would be correct. 
What is the best way to interpolate daily values to provide a smooth curve while maintaining monthly totals?
Jan 50
Feb 60
Mar 85
Apr 98
May 111
Jun 113
Jul 113
Aug 105
Sep 91
Oct 75
Nov 54
Dec 45

 A: A possible idea : define a table of $X_i$ and $Y_i$ such that $X_i$ represents the number of days from January 1st and $Y_i$ the cumulated values from  January 1st.  
So $X_0=0$, $Y_0=0$, then $X_1=30$, $Y_1=50$, then $X_2=30+28=58$, $Y_2=50+60=110$, then $X_3=58+31=89$, $Y_3=110+85=195$ and so on up to the end of the year. This should give you something like
   0       0
  30      30 
  58     110
  89     195
 119     293
 150     404
 180     517
 211     630
 242     735
 272     826
 303     901
 333     955
 364    1000

Using your data shows a very nice and smooth curve for function $Y(X)$
Using now cubic splines : cumulated values (the $Y$'s) will be respected. Otherwise, use any other standard interpolation technique.
Now, as an example : you want to know the value for day $251$; interpolating for $X=250$ gives $Y=760.606$;  interpolating for $X=251$ gives $Y=763.747$; so $763.747-760.606=3.141$. Isn't funny to find, as a result of a random calculation something lookig like $\pi$ ?
