<p>Some of my more interesing answers, not necessary most upvoted:</p>

<p><a href="http://stats.stackexchange.com/q/123651/22228">Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$</a></p>

<p><a href="http://stats.stackexchange.com/a/130200/22228">What is the distribution of R2 in linear regression under the null hypothesis?</a> My answer includes a comprehensive graphic of the distribution of $R^2$ for multiple regression on a small sample.</p>

<p><a href="http://stats.stackexchange.com/q/131400/22228">Ink to data ratio and plot backgrounds</a> - a fascinating question about the recent trend for plots to have grey backgrounds.</p>

<p><a href="http://stats.stackexchange.com/a/125368/22228">Uniform random variable as sum of two random variables</a> - if $U$ is a uniform variable, why can't we find i.i.d. variables $X$ and $Y$ such that $U=X+Y$? A nice solution by thinking about limits on kurtosis.</p>

<p><a href="http://stats.stackexchange.com/a/139683/22228">Random walk on the edges of a cube</a> - if a spider walks at random along the edges, what is the expected number of steps to reach an ant trapped on the opposite vertex? Parity considerations give an elementary pen-and-paper method.</p>

<p><a href="http://stats.stackexchange.com/a/125575/22228">What does an Added Variable Plot (Partial Regression Plot) explain in a multiple regression?</a></p>

<p><a href="http://stats.stackexchange.com/q/119835/22228">Correlation between a nominal (IV) and a continuous (DV) variable</a> - sometimes we have to explain that something can't be done, but suggest alternatives or analogues.</p>

<p><a href="http://stats.stackexchange.com/q/133072/22228">Finding an unbiased estimator with the smallest variance</a> - answered with Lagrange multipliers.</p>

<p><a href="http://stats.stackexchange.com/a/122572/22228">Prove the equivalence of the following two formulas for Spearman correlation</a> - using only high school methods. This is a bit clunky, but the topic sometimes comes up at high school level (at least in my country), so it's nice not to have to rely on higher level maths.</p>

<p><a href="http://stats.stackexchange.com/q/74147/22228">Expectation of Quotient of Sums of IID Random Variables (Cambridge University Worksheet)</a> - an interesting question that can be answered by (a)symmetry considerations.</p>

<p><a href="http://stats.stackexchange.com/a/125678/22228">Transformation Chi-squared to Normal distribution</a> - including a trick using a Rademacher variable, and some very pretty graphs to show deciles (and R code).</p>

<p>Addressing some elementary misconceptions about summary statistics, with nice counterexamples: <a href="http://stats.stackexchange.com/a/125096/22228">Does mean = median imply that a unimodal distribution is symmetric?</a> and <a href="http://stats.stackexchange.com/a/135742/22228">Will two distributions with identical 5-number summaries always have the same shape?</a></p>

Silverfish