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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 统计代写|生物统计代写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 $\mathrm{I}$ 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 $\mathrm{I}$.

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
• $$• \sigma^2=\frac{\text { sum of all }(\text { deviations from } \mu)^2}{N}=\frac{\sum(X-\mu)^2}{N} •$$
• 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.
$$\mathrm{IQR}=75 \text { th percentile }-25 \text { th percentile }=X_{75}-X_{25}$$

## 统计代写|生物统计代写Biostatistics代考|The Coefficient of Variation

The standard deviations of two populations resulting from measuring the same variable can be compared to determine which of the two populations is more variable. That is, when one standard deviation is substantially larger than the other (i.e., more than two times as large), then clearly the population with the larger standard deviation is much more variable than the other. It is also important to be able to determine whether a single population is highly variable or not. A parameter that measures the relative variability in a population is the coefficient of variation. The coefficient of variation will be denoted by $\mathrm{CV}$ and is defined to be
$$\mathrm{CV}=\frac{\sigma}{|\mu|}$$
The coefficient of variation is also sometimes represented as a percentage in which case
$$\mathrm{CV}=\frac{\sigma}{|\mu|} \times 100 \%$$

The coefficient of variation compares the size of the standard deviation with the size of the mean. When the coefficient of variation is small, this means that the variability in the population is relatively small compared to the size of the mean of the population. On the other hand, when the coefficient of variation is large, this indicates that the population varies greatly relative to the size of the mean. The standard for what is a large coefficient of variation differs from one discipline to another, and in some disciplines a coefficient of variation of less than $15 \%$ is considered reasonable, and in other disciplines larger or smaller cutoffs are used.

Because the standard deviation and the mean have the same units of measurement, the coefficient of variation is a unitless parameter. That is, the coefficient is unaffected by changes in the units of measurement. For example, if a variable $X$ is measured in inches and the coefficient of variation is $\mathrm{CV}=2$, then coefficient of variation will also be 2 when the units of measurement are converted to centimeters. The coefficient of variation can also be used to compare the relative variability in two different and unrelated populations; the standard deviation can only be used to compare the variability in two different populations based on similar variables.

# 生物统计代考

## 统计代写|生物统计代写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 $\sigma^2$ 或者 $\operatorname{Var}(X)$. 变量的方差 $X$
• 在由以下人员组成的总体上测量 $N$ 单位是
• $\$ \• \backslash \operatorname{sigma}^{\wedge} 2=\backslash\left{\begin{aligned} & \end{aligned}\right. • \\ • 总体的标准差定义为方差的平方根，表示为 \sigma 或者 \mathrm{SD}(X).
\operatorname{SD}(X)=\sigma=\sqrt{\sigma^2}=\sqrt{\operatorname{Var}(X)}
$$• 人口的四分位距是第 25 和第 75 个百分位数之间的距离，用 IQR 表示。$$
\text { IQR }=75 \text { th percentile }-25 \text { th percentile }=X_{75}-X_{25}
$$## 统计代写|生物统计代写Biostatistics代考|The Coefficient of Variation 可以比较由测量相同变量产生的两个总体的标准偏差，以确定两个总体中的哪一个更具可变性。也就是说，当一个标准差明显大于另一个时（即两倍以上），那 么显然具有较大标准差的总体比另一个具有更大的可变性。能够确定单个总体是否具有高度可变性也很重要。衡量总体相对变异性的参数是变异系数。变异系数 将表示为CV并且被定义为$$
\mathrm{CV}=\frac{\sigma}{|\mu|}
$$变异系数有时也表示为百分比，在这种情况下$$
\mathrm{CV}=\frac{\sigma}{|\mu|} \times 100 \%


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## MATLAB代写

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