Distribution of estimated statistics from different samples (same size) from the same population is called a sampling distribution
This is called a sampling distribution not a sample distribution
It permits to make probability judgement about samples.
Because of the central limit theorem, sampling distributions are known to be normal and therefore are fundamental to inferential statistics because they allow for probabilistic predictions about outcomes.
The code below showcase the fact that a sample distribution created from the mean of a lot of sample from the same population has a normal form.
population_n = 10000;
population_data = [];
population_max = 100;
population_data = [];
for (i = 0; i < population_n; i++) {
random_value = Math.floor(Math.random() * Math.floor(population_max));
population_data.push(random_value);
}
histogram({ selector: "population", data: population_data});
// Sample Data
sample_distribution_data = [];
sample_distribution_n = 1000;
for (j = 0; j < sample_distribution_n; j++) {
sample_data = [];
sample_n = 20;
for (i = 0; i < sample_n; i++) {
population_random_index = Math.floor(
Math.random() * Math.floor(population_max)
);
sample_data.push(population_data[population_random_index]);
}
sample_distribution_data.push(d3.mean(sample_data));
}
histogram({ selector: "sample", data:sample_distribution_data});