Python实现平均数抽样分布

Python中实现平均数抽样分布通常涉及到统计学中的中心极限定理，它指出当样本量足够大时，样本均值的分布近似于正态分布，无论总体分布是什么样的。你可以使用numpy库中的random模块来模拟这个过程。

首先，你需要导入必要的库，然后创建一个函数来生成大量的样本均值。这里是一个简单的示例：

import numpy as np

def sample_mean_distribution(n_samples, n_trials, population_mean, population_std_dev):
    sample_means = []
    
    for _ in range(n_trials):
        # 从正态分布中随机抽取n_samples个样本
        samples = np.random.normal(population_mean, population_std_dev, size=n_samples)
        
        # 计算样本均值并添加到列表中
        sample_means.append(np.mean(samples))
    
    # 将样本均值转换为数组并计算频率分布或直方图
    histogram, bin_edges = np.histogram(sample_means, bins='auto')
    
    return sample_means, histogram

# 示例参数设置
population_mean = 0
population_std_dev = 1
n_samples = 50
n_trials = 10000

sample_means, distribution = sample_mean_distribution(n_samples, n_trials, population_mean, population_std_dev)
mean_of_sample_means = np.mean(sample_means)

print(f"Sample means and their frequency:")
print(distribution)
print(f"\nMean of the sample means: {mean_of_sample_means}")

在这个例子中，`sample_mean_distribution`函数会返回每次试验的样本均值以及它们的频数分布。你可以通过改变`n_trials`来观察随着更多样本的增加，均值分布是如何接近正态分布的。