### 统计代写|商业分析作业代写Statistical Modelling for Business代考|Describing Central Tendency

• 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

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The mean, median, and mode

In addition to describing the shape of the distribution of a sample or population of measurements, we also describe the data set’s central tendency. A measure of central tendency represents the center or middle of the data. Sometimes we think of a measure of central tendency as a typical value. However, as we will see, not all measures of central tendency are necessarily typical values.

One important measure of central tendency for a population of measurements is the population mean. We define it as follows:More precisely, the population mean is calculated by adding all the population measurements and then dividing the resulting sum by the number of population measurements. For instance, suppose that Chris is a college junior majoring in business. This semester Chris is taking five classes and the numbers of students enrolled in the classes (that is, the class sizes) are as follows:

The mean $\mu$ of this population of class sizes is
$$\mu=\frac{60+41+15+30+34}{5}=\frac{180}{5}=36$$
Because this population of five class sizes is small, it is possible to compute the population mean. Often, however, a population is very large and we cannot obtain a measurement for each population element. Therefore, we cannot compute the population mean. In such a case, we must estimate the population mean by using a sample of measurements.

In order to understand how to estimate a population mean, we must realize that the population mean is a population parameter.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The Car Mileage Case: Estimating Mileage

In order to offer its tax credit, the federal government has decided to define the “typical” EPA combined city and highway mileage for a car model as the mean $\mu$ of the population of EPA combined mileages that would be obtained by all cars of this type. Here, using the mean to represent a typical value is probably reasonable. We know that some individual cars will get mileages that are lower than the mean and some will get mileages that are above it. However, because there will be many thousands of these cars on the road, the mean mileage obtained by these cars is probably a reasonable way to represent the model’s overall fuel economy. Therefore, the government will offer its tax credit to any automaker selling a midsize model equipped with an automatic transmission that achieves a mean EPA combined mileage of at least $31 \mathrm{mpg}$.

To demonstrate that its new midsize model qualifies for the tax credit, the automaker in this case study wishes to use the sample of 50 mileages in Table $3.1$ to estimate $\mu$, the model’s mean mileage. Before calculating the mean of the entire sample of 50 mileages, we will illustrate the formulas involved by calculating the mean of the first five of these mileages.

Table $3.1$ tells us that $x_{1}=30.8, x_{2}=31.7, x_{3}=30.1, x_{4}=31.6$, and $x_{5}=32.1$, so the sum of the first five mileages is
\begin{aligned} \sum_{i=1}^{5} x_{i} &=x_{1}+x_{2}+x_{3}+x_{4}+x_{5} \ &=30.8+31 . \overline{3}+30.1+31.6+3 \overline{2} .1=156.3 \end{aligned}
Therefore, the mean of the first five mileages is
$$\bar{x}=\frac{\sum_{i=1}^{5} x_{i}}{5}=\frac{156.3}{5}=31.26$$
Of course, intuitively, we are likely to obtain a more accurate point estimate of the population mean by using all of the available sample information. The sum of all 50 mileages can be verified to be
$$\sum_{i=1}^{50} x_{i}=x_{1}+x_{2}+\cdots+x_{50}=30.8+31.7+\cdots+31.4=1578$$
Therefore, the mean of the sample of 50 mileages is
$$\bar{x}=\frac{\sum_{i=1}^{50} x_{i}}{50}=\frac{1578}{50}=31.56$$
This point estimate says we estimate that the mean mileage that would be obtained by all of the new midsize cars that will or could potentially be produced this year is $31.56 \mathrm{mpg}$. Unless we are extremely lucky, however, there will be sampling error. That is, the point estimate $\bar{x}=31.56$ mpg, which is the average of the sample of fifty randomly selected mileages, will probably not exactly equal the population mean $\mu$, which is the average mileage that would be obtained by all cars. Therefore, although $\bar{x}=31.56$ provides some evidence that $\mu$ is at least 31 and thus that the automaker should get the tax credit, it does not provide definitive evidence. In later chapters, we discuss how to assess the reliability of the sample mean and how to use a measure of reliability to decide whether sample information provides definitive evidence.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Comparing the mean, median, and mode

Often we construct a histogram for a sample to make inferences about the shape of the sampled population. When we do this, it can be useful to “smooth out” the histogram and use the resulting relative frequency curve to describe the shape of the population. Relative frequency curves can have many shapes. Three common shapes are illustrated in Figure $3.3$. Part (a) of this figure depicts a population described by a symmetrical relative frequency curve. For such a population, the mean $(\mu)$, median $\left(M_{s}\right)$, and mode $\left(M_{s}\right)$ are all equal. Note that in this case all three of these quantities are located under the highest point of the curve. It follows that when the frequency distribution of a sample of measurements is approximately symmetrical, then the sample mean, median, and mode will be nearly the same. For instance,

consider the sample of 50 mileages in Table 3.1. Because the histogram of these mileages in Figure $3.2$ is approximately symmetrical, the mean $-31.56$ – and the median-31.55- of the mileages are approximately equal to each other.

Figure $3.3$ (b) depicts a population that is skewed to the right. Here the population mean is larger than the population median, and the population median is larger than the population mode (the mode is located under the highest point of the relative frequency curve). In this case the population mean averages in the large values in the upper tail of the distribution. Thus the population mean is more affected by these large values than is the population median. To understand this, we consider the following example.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The mean, median, and mode

μ=60+41+15+30+345=1805=36

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The Car Mileage Case: Estimating Mileage

∑一世=15X一世=X1+X2+X3+X4+X5 =30.8+31.3¯+30.1+31.6+32¯.1=156.3

X¯=∑一世=15X一世5=156.35=31.26

∑一世=150X一世=X1+X2+⋯+X50=30.8+31.7+⋯+31.4=1578

X¯=∑一世=150X一世50=157850=31.56

## 广义线性模型代考

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## 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。