# What's the meaning of using Bootstrap? Why should resampling from sample set have any difference? [duplicate]

I just learned Bootstrap Method from my Statistics course. The teacher says that the whole population is unknown, however we have some sample set $$\mathcal{D}$$ with sample size $$N$$. Then we use this sample set $$\mathcal{D}$$ as population and sample from $$\mathcal{D}$$ with replacement to compute all statistics we want (like mean, variance, median, or train a ML model from resampled set, etc.). We will have a fantatic result from this method (average result from all resampled sets).

However, I totally cannot understand the spirit of resampling from $$\mathcal{D}$$. For example, the actual distribution is Bernoulli distribution with $$p = 0.5$$. I get a sample set $$\mathcal{D}$$ with sample size $$100$$ from this distribution with $$52$$ of one and $$48$$ of zero. If I resample with replacement from $$\mathcal{D}$$, it just means that I have a Bernoulli distribution with $$p = 0.52$$.

My Questions:

1. Why shouldn't I directly compute all statistics I want from $$\mathcal{D}$$? No matter how many times of resampling, I can only get converged $$\text{mean} = 0.52$$ and $$\text{var} = 0.52 * 0.48$$. I don't think I can get any improvement from resampling or I can even recover the underlying distribution. Am I right?

2. What's the loophole of my arguments? What's the advantage of Bootstrap? For example, is there anything I cannot get from sample set $$\mathcal{D}$$ but from $$Bootstrap$$?

The main application of the bootstrap is to learn something about the sampling distribution of the statistic, not the statistic itself. While it is easy to calculate an estimate $$\hat D$$ of the ratio $$D$$ of two medians from data, there might not be a reliable formula for its standard error $$\sqrt{\text{Var}(\hat D)}$$. You would need that to construct simple confidence intervals. The bootstrap provides you with methods to estimate measures like $$\sqrt{\text{Var}(\hat D)}$$.