How does bagging help reduce the variance

I learned that bagging helps reduce variance by averaging but I couldn't understand this. Can someone explain this intuitively?

High Variance - Model varies a lot on small changes
High Bias - Model doesn't vary so much but predict quite away from the truth

Let's check a Decision Tree on 5 values - $$\begin{array} {|r|r|} \hline 1 &5 &10 &15 &20\\ \hline \end{array}$$ In this tree split,
Value of 9.9 will be 7.5
Value of 10.1 will be 12.5.
Showing a very high variance.

Let's create 4 Random Tree of 3 elements each - $$\begin{array} {|r|r|} \hline Tree-1 &5 &10 &15\\ \hline Tree-2 &1 &15 &20\\ \hline Tree-3 &1 &05 &20\\ \hline Tree-4 &5 &15 &20\\ \hline \end{array}$$ Value of 9.9 = (7.5 + 7.5 + 12.5 + 10)/4 ~ 9.375
Value of 10.1 = (12.5 + 7.5 + 12.5 + 10)/4 ~ 10.625
Variance is reduced a lot.

In bagging, we build multi-hundreds of the Tree(Can build other models too which offers high variance) which results in a large variance reduction

• can you please elaborate more how Value of 9.9 will be 7.5? how 7.5 is calculated? and another matter, in bagging the generated dataset size will be same as the original, so here the original one has 5 elements while the bagging used has only 3 elements? Jul 31 at 1:50