title: Smoothing Small Data Set With Second Order Quadratic Curve
body: <p>I'm doing some specific signal analysis, and I am in need of a method that would smooth out a given bell-shaped distribution curve. A running average approach isn't producing the results I desire. I want to keep the min/max, and general shape of my fitted curve intact, but resolve the inconsistencies in sampling.</p>
  
  <p>In short: if given a set of data that models a simple quadratic curve, what statistical smoothing method would you recommend?</p>
  
  <p>If possible, please reference an implementation, library, or framework.</p>
  
  <p>Thanks SO!</p>
  
  <p><strong>Edit</strong>: Some helpful data</p>
  
  <p>(A possible signal graph)</p>
  
  <p><a href="https://i.stack.imgur.com/dnc9Z.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/dnc9Z.png" alt="alt text"></a>
  </p>
  
  <p>The dark colored quadratic is my "fitted" curve of the light colored connected data points.</p>
  
  <p>The sample @ -44 (approx.), is a problem in my graph (i.e. a potential sample inconsistency). I need this curve to "fit" the distribution better, and overcome the values that do not trend accordingly. Hope this helps!</p>