title: Is there a function to determine dataset (discrete scale, 1 to 5) if number of data points, mean, and standard deviation is known?
body: <p>My question is very similar to this question: <a href="https://stackoverflow.com/questions/3208299/reverse-statistics-generating-data-based-on-mean-and-standard-deviation">&quot;Reverse&quot; statistics</a>. They, however, want to create a <em>normal</em> (and random) distribution of <em>arbitrary</em> size that fits a certain mean and standard deviation. Let's say, however, that we know <em>more than</em> the mean and std. deviation, that we know the <strong>number of data points</strong> as well as the <strong>discrete scale</strong> the values fall on.</p>
  <p>So I really have two questions. <strong>First</strong>, given we know,</p>
  <ul>
  <li>mean</li>
  <li>standard deviation</li>
  <li>n</li>
  <li>discrete scale of 1 to 5 (i.e., values can only be 1, 2, 3, 4, or 5)</li>
  </ul>
  <p>...is it possible to know the exact dataset? For example, if we know that there are 5 data points on a 1–5 Likert scale, and the mean is 4.40 and the standard deviation is 1.20, is it possible to figure out that the data set is {5, 5, 5, 5, 2} (order of values not being important)?</p>
  <p><strong>Second</strong>, is there a function already out there to automatically solve this problem?</p>