### 统计代写|商业分析作业代写Statistical Modelling for Business代考|Cumulative distributions and ogives

• 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|Cumulative distributions and ogives

Another way to summarize a distribution is to construct a cumulative distribution. To do this, we use the same number of classes, the same class lengths, and the same class boundaries that we have used for the frequency distribution of a data set. However, in order to construct a cumulative frequency distribution, we record for each class the number of

measurements that are less than the upper boundary of the class. To illustrate this idea, Table $2.10$ gives the cumulative frequency distribution of the payment time distribution summarized in Table $2.7$ (page 64). Columns (1) and (2) in this table give the frequency distribution of the payment times. Column (3) gives the cumulative frequency for each class. To see how these values are obtained, the cumulative frequency for the class $10<13$ is the number of payment times less than 13 . This is obviously the frequency for the class $10<13$, which is 3 . The cumulative frequency for the class $13<16$ is the number of payment times less than 16 , which is obtained by adding the frequencies for the first two classes-that is, $3+14=17$. The cumulative frequency for the class $16<19$ is the number of payment times less than 19-that is, $3+14+23=40$. We see that, in general, a cumulative frequency is obtained by summing the frequencies of all classes representing values less than the upper buumdary of the class.

Column (4) gives the cumulative relative frequency for each class, which is obtained by summing the relative frequencies of all classes representing values less than the upper boundary of the class. Or, more simply, this value can be found by dividing the cumulative frequency for the class by the total number of measurements in the data set. For instance, the cunulative relative frequency for the class $19<22$ is $52 / 65-.8$. Culum (5) gives the cumulative percent frequency for each class, which is obtained by summing the percent frequencies of all classes representing values less than the upper boundary of the class. More simply, this value can be found by multiplying the cumulative relative frequency of a class by 100. For instance, the cumulative percent frequency for the class $19<22$ is $.8 \times(100)=80$ percent.

As an example of interpreting Table $2.10 .60$ of the 65 payment times are 24 days or less. or, equivalently, $92.31$ percent of the payment times (or a fraction of $.9231$ of the payment times) are 24 days or less. Also, notice that the last entry in the cumulative frequency distribution is the total number of measurements (here, 65 payment times). In addition, the last entry in the cumulative relative frequency distribution is $1.0$ and the last entry in the cumulalive percent frequency disiribution is $100 \%$. In general, for any dala sel, these lasi eniries will be, respectively, the total number of measurements, $1.0$, and $100 \%$.

An ogive (pronounced “oh-jive”) is a graph of a cumulative distribution. To construct a frequency ogive, we plot a point above each upper class boundary at a height equal to the cumulative frequency of the class. We then connect the plotted points with line segments. A similar graph can be drawn using the cumulative relative frequencies or the cumulative percent frequencies. As an example, Figure $2.14$ gives a percent frequency ogive of the payment times. Looking at this figure, we see that, for instance, a little more than 25 percent (actually, $26.15$ percent according to Table $2.10$ ) of the payment times are less than 16 days, while 80 percent of the payment times are less than 22 days. Also notice that we have completed the ogive by plotting an additional point at the lower boundary of the first (leftmost) class at a height equal to zero. This depicts the fact that none of the payment times is less than 10 days. Finally, the ogive graphically shows that all ( 100 percent) of the payment times are less than 31 days.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Dot Plots

A very simple graph that can be used to summarize a data set is called a dot plot. To make a dot plot we draw a horizontal axis that spans the range of the measurements in the data set. We then place dots above the horizontal axis to represent the measurements. As an example, Figure $2.18$ (a) shows a dot plot of the exam scores in Table $2.8$ (page 68). Remember, these are the scores for the first exam given before implementing a strict attendance policy. The horizontal axis spans exam scores from 30 to 100 . Each dot above the axis represents an exam score. For instance, the two dots above the score of 90 tell us that two students received a 90 on the exam. The dot plot shows us that there are two concentrations of scores-those in the $80 \mathrm{~s}$ and $90 \mathrm{~s}$ and those in the $60 \mathrm{~s}$. Figure $2.18(\mathrm{~b})$ gives a dot plot of the scores on the second exam (which was given after imposing the attendance policy). As did the percent frequency polygon for Exam 2 in Figure $2.13$ (page 69), this second dot plot shows that the attendance policy eliminated the concentration of scores in the $60 \mathrm{~s}$.

Dot plots are useful for detecting outliers, which are unusually large or small observations that are well separated from the remaining observations. For example, the dot plot for exam 1 indicates that the score 32 seems unusually low. How we handle an outlier depends on its cause. If the outlier results from a measurement error or an error in recording or processing the data, it should be corrected. If such an outlier cannot be corrected, it should be discarded. If an outlier is not the result of an error in measuring or recording the data, its cause may reveal important information. For example, the outlying exam score of 32 convinced the author that the student needed a tutor. After working with a tutor, the student showed considerable improvement on Exam 2. A more precise way to detect outliers is presented in Section 3.3.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|back-to-back stem-and-leaf display

If we wish to compare two distributions, it is convenient to construct a back-to-back stemand-leaf display. Figure $2.20$ presents a back-to-back stem-and-leaf display for the previously discussed exam scores. The left side of the display summarizes the scores for the first exam. Remember, this exam was given before implementing a strict attendance policy. The right side of the display summarizes the scores for the second exam (which was given after imposing the attendance policy). Looking at the left side of the display, we see that for the first exam there are two concentrations of scores-those in the $80 \mathrm{~s}$ and $90 \mathrm{~s}$ and those in the $60 \mathrm{~s}$. The right side of the display shows that the attendance policy eliminated the concentration of scores in the $60 \mathrm{~s}$ and illustrates that the scores on exam 2 are almost single peaked and somewhat skewed to the left.

Stem-and-leaf displays are useful for detecting outliers, which are unusually large or small observations that are well separated from the remaining observations. For example, the stem-and-leaf display for exam 1 indicates that the score 32 seems unusually low. How we handle an outlier depends on its cause. If the outlier results from a measurement error or an error in recording or processing the data, it should be corrected. If such an outlier cannot be corrected, it should be discarded. If an outlier is not the result of an error in measuring or recording the data, its cause may reveal important information. For example, the outlying exam score of 32 convinced the author that the student needed a tutor. After working with a tutor, the student showed considerable improvement on exam 2. A more precise way to detect outliers is presented in Section 3.3.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Cumulative distributions and ogives

ogive（发音为“oh-jive”）是累积分布图。为了构建频率曲线，我们在每个上层类边界上方绘制一个点，高度等于类的累积频率。然后我们将绘制的点与线段连接起来。可以使用累积相对频率或累积百分比频率绘制类似的图表。例如，图2.14给出支付时间的百分比频率。看看这个数字，我们看到，例如，略高于 25%（实际上，26.15根据表百分比2.10) 的付款时间少于 16 天，而 80% 的付款时间少于 22 天。另请注意，我们通过在第一个（最左边）类的下边界处绘制一个附加点，高度为零，从而完成了 ogive。这描述了没有一个付款时间少于 10 天的事实。最后，ogive 以图形方式显示所有（100%）的付款时间都少于 31 天。

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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。