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# 澳洲代考|生物统计学代考Biostatistics代考|MPH6041

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## 澳洲代考|生物统计学代考Biostatistics代考|Parameters Measuring Centrality

The two parameters in the population of values of a quantitative variable that summarize how the variable is distributed are the parameters that measure the typical or central values in the population and the parameters that measure the spread of the values within the population. Parameters describing the central values in a population and the spread of a population are often used for summarizing the distribution of the values in a population; however, it is important to note that most populations cannot be described very well with only the parameters that measure centrality and the spread of the population.

Measures of centrality, location, or the typical value are parameters that lie in the “center” or “middle” region of a distribution. Because the center or middle of a distribution is not easily determined due to the wide range of different shapes that are possible with a distribution, there are several different parameters that can be used to describe the center of a population. The three most commonly used parameters for describing the center of a population are the mean, median, and mode. For a quantitative variable $X$.

• The mean of a population is the average of all of the units in the population, and will be denoted by $\mu$. The mean of a variable $X$ measured on a population consisting of $N$ units is
$$\mu=\frac{\text { sum of the values of } X}{N}=\frac{\sum X}{N}$$
• The median of a population is the 50 th percentile of the population, and will be denoted by $\tilde{\mu}$. The median of a population is found by first listing all of the values of the variable $X$, including repeated $X$ values, in ascending order. When the number of units in the population (i.e., $N$ ) is an odd number, the median is the middle observation in the list of ordered values of $X$; when $N$ is an even number, the median will be the average of the two observations in the middle of the ordered list of $X$ values.
• The mode of a population is the most frequent value in the population, and will be denoted by $M$. In a graph of the probability density function, the mode is the value of $X$ under the peak of the graph, and a population can have more than one mode as shown in Figure 2.8.

## 澳洲代考|生物统计学代考Biostatistics代考|Measures of Dispersion

While the mean, median, and mode of a population describe the typical values in the population, these parameters do not describe how the population is spread over its range of values. For example, Figure $2.16$ shows two populations that have the same mean, median, and mode but different spreads.

Even though the mean, median, and mode of these two populations are the same, clearly, population I is much more spread out than population II. The density of population II is greater at the mean, which means that population II is more concentrated at this point than population I.

When describing the typical values in the population, the more variation there is in a population the harder it is to measure the typical value, and just as there are several ways of measuring the center of a population there are also several ways to measure the variation in a population. The three most commonly used parameters for measuring the spread of a population are the variance, standard deviation, and interquartile range. For a quantitative variable $X$

• the variance of a population is defined to be the average of the squared deviations from the mean and will be denoted by $\sigma^{2}$ or $\operatorname{Var}(X)$. The variance of a variable $X$ measured on a population consisting of $N$ units is
$$\sigma^{2}=\frac{\text { sum of all(deviations from } \mu)^{2}}{N}=\frac{\sum(X-\mu)^{2}}{N}$$
• the standard deviation of a population is defined to be the square root of the variance and will be denoted by $\sigma$ or $\operatorname{SD}(X)$.
$$\operatorname{SD}(X)=\sigma=\sqrt{\sigma^{2}}=\sqrt{\operatorname{Var}(X)}$$
• the interquartile range of a population is the distance between the 25 th and 75 th percentiles and will be denoted by IQR.
$$\mathrm{IQR}=75 \text { th percentile }-25 \text { th percentile }=X_{75}-X_{25}$$

## 澳洲代考|生物统计学代考BIOSTATISTICS代考|PARAMETERS MEASURING CENTRALITY

• 总体的平均值是总体中所有单位的平均值，表示为μ. 变量的平均值X在由以下人员组成的总体上测量ñ单位是
μ= 的值的总和 Xñ=∑Xñ
• 人口的中位数是人口的第 50 个百分位，表示为μ~. 通过首先列出变量的所有值来找到总体的中位数X，包括重复X值，按升序排列。当人口中的单位数量一世.和.,$ñ$是奇数，中位数是有序值列表中的中间观察值X; 什么时候ñ是偶数，中位数将是有序列表中间的两个观察值的平均值X价值观。
• 人口的众数是人口中出现频率最高的值，记为米. 在概率密度函数图中，众数是X如图 2.8 所示，一个总体可以有多个众数。

## 澳洲代考|生物统计学代考BIOSTATISTICS代考|MEASURES OF DISPERSION

• 总体的方差定义为与均值的平方偏差的平均值，并表示为σ2或者曾是⁡(X). 变量的方差X在由以下人员组成的总体上测量ñ单位是
σ2= 所有的总和（偏离 μ)2ñ=∑(X−μ)2ñ
• 总体的标准差定义为方差的平方根，表示为σ或者标清⁡(X).
标清⁡(X)=σ=σ2=曾是⁡(X)
• 人口的四分位距是第 25 和第 75 个百分位数之间的距离，用 IQR 表示。
我问R=75 百分位数 −25 百分位数 =X75−X25

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。