数理统计的基本概念
数理统计是指在数学的指导下，对于由观察、实验或其他手段收集到的数据进行处理、分析和推断的一门科学。它不仅仅局限于简单的数据汇总，更重要的是通过各种统计方法，来描述现象、预测未来和解释因果关系。
统计资料的收集与整理
在进行数理统计分析之前，首先需要收集到相关的原始数据，这些数据可能来自于调查问卷、实验记录或者历史文件等。在此基础上，我们还需要对这些数据进行清洗和整理，以确保所使用的样本是代表性且准确无误的。这通常涉及去除重复项、填补缺失值以及处理异常值等操作。
描述性统计量与图表
描述性统计量是用来描述一个变量或一组变量主要特征的一种方法，它可以帮助我们快速地了解样本分布情况。常见的描述性统计量包括平均数、中位数、中位夹带差距（IQR）、四分位数范围等。此外，通过绘制直方图、箱线图等图形，可以直观地展示出变量分布的情况，从而更好地理解并传达信息。
推断性研究与假设检验
推断性的研究旨在基于已有的样本数据，对未知参数或人口比例做出概率性的推测。其中，假设检验是一个重要工具，它允许我们根据某个假设是否得到了足够支持来做出结论。例如，在药物临床试验中，我们可以提出一个假设，即新药比安慰剂更加有效，并通过抽取随机控制组和治疗组，然后计算置信区间，看看其是否覆盖了零值，从而得出结论。
inferential statistics and hypothesis testing in practice
Inferential statistics is a powerful tool for making generalizations about populations based on sample data. It allows us to draw conclusions about the population from which the sample was drawn, rather than just describing the characteristics of the sample itself.
Hypothesis testing is a specific type of inferential statistical procedure that involves testing an hypothesis or assumption about a population parameter against alternative hypotheses or assumptions.
For example, let's say we are interested in comparing the mean heights of men and women in two different countries. We could take random samples of men and women from each country, calculate their means, and then use hypothesis testing to determine whether there is a statistically significant difference between them.
By using inferential statistics and hypothesis testing together with other statistical methods such as regression analysis, time series analysis etc., we can gain valuable insights into complex real-world problems by making informed decisions based on our findings