&gt; <i>The std. dev. of a binomial is sqrt(n p (1-p)). So for 19 coin flips that&#x27;s ~2.2, or 11%, not 23%.</i><p>You are correct.  The usual way in which std dev is applied is  ± sigma accounts for about 68% of the trials, which is 2 std deviations, and is what I had in mind.
So for 19 people flipping a coin, you&#x27;ll have a range of about 23% variation.<p>That factor of 2 does not change the message.