Bias and variance in KNN and decision trees According to the bias and variance formulas in classification problems( Machine learning)
What evidence gives the fact that having few data points give low bias and high variance
And having more data points give high bias and low variance
 A: Fewer neighbors usually mean closer neighbors (unless there are multiple close neighbors with equal distance from the point of interest $x_0$). Modelling $x_0$ as a function of only the few closest neighbors, i.e. the most similar data points, allows for high flexibility (utilizing the features of the closest data points but not the ones farther apart) and thus low bias but high variance. Including more neighbors results in less flexibility (higher smootheness, utilizing the features of not only the closest data points but also the ones farther apart) and thus higher bias but lower variance.
Take an extreme example: I can model you as equalling your twin brother or a person that is the most similar to you in the whole world ($k=1$). This is highly flexible (low bias), but relying on a single data point is very risky (high variance). Or I can model you as an average (in regression) or mode (in classification) of all the people on the planet ($k=N$). This is highly inflexible (high bias) but very robust (low variance).
