### 统计代写|AP统计辅导AP统计答疑|Exploring and Graphing Univariate Data

AP统计学与大学的统计学课程在核心内容上是一致的，只是涉及的深度稍浅，AP统计学主要包含以下四部分内容。 第一部分 如何获取数据，获取数据的方式有哪些呢？ 获取数据的方式主要包括普查、抽样调查、观测研究和实验设计等。

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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

## 统计代写|AP统计辅导AP统计答疑|Describing Distributions

• The organization of data into graphical displays is essential to understanding statistics. This chapter discusses how to describe distributions and various types of graphs used for organizing univariate data. The types of graphs include modified boxplots, histograms, stem-and-leaf plots, bar graphs, dotplots, and pie charts. Students in AP Statistics should have a clear understanding of what a variable is and the types of variables that are encountered.
• A variable is a characteristic of an individual and can take on different values for different individuals. Two types of variables are discussed in this chapter: categorical variables and quantitative variables.

Categorical variable: Places an individual into a category or group Quantitative variable: Takes on a numerical value

Variables may take on different values. The pattern of variation of a variable is its distribution. The distribution of a variable tells us what values the variable takes and how often it takes each value.

• When describing distributions, it’s important to describe what you see in the graph. It’s important to address the shape, center, and spread of the distribution in the context of the problem.
• When describing shape, focus on the main features of the distribution. Is the graph approximately symmetrical, skewed left, or skewed right?

## 统计代写|AP统计辅导AP统计答疑|Standard Deviation

$$s=\sqrt{2.5} \approx 1.5811$$
It’s probably more important to understand the concept of what standard deviation means than to be able to calculate it by hand. Our trusty calculators or computer software can handle the calculation for us. Understanding what the number means is what’s most important. It’s worth noting that most calculators will give two values for standard deviation. One is used when dealing with a population, and the other is used when dealing with a sample. The TI $83 / 84$ calculator shows the population standard deviation as $x$ and the sample standard deviation as $S_{x}$. A population is all individuals of interest, and a sample is just part of a population. We’ll discuss the concept of population and different types of samples in later chapters.

• It’s also important to address any outliers that might be present in the distribution. Outliers are values that fall outside the overall pattern of the distribution. It is important to be able to identify potential outliers in a distribution, but we also want to determine whether or not a value is mathematically an outlier.
• Example 4: Consider Data Set B, which consists of test scores from a college statistics course:
\begin{aligned} &98,36,67,85,79,100,88,85,60,69,93,58,65,89,88,71,79,85,73,87, \ &81,77,76,75,76,73 \end{aligned}
1. Arrange the data in ascending order.
\begin{aligned} &36,58,60,65,67,69,71,73,73,75,76,76,77,79,79,81,85,85,85,87, \ &88,88,89,93,98,100 \end{aligned}Find the median (average of the two middle numbers): 78 .
2. Find the median of the first half of numbers. This is the first quartile, $\mathrm{Q}_{1}: 71$.
3. Find the median of the second half of numbers, the third quartile, $\mathrm{Q}_{3}: 87$.
4. Find the interquartile range (IQR): $I Q R=Q_{3}-Q_{1}=87-71=16$.
5. Multiply the IQR by $1.5: 16 \times 1.5=24$.
6. Add this number to $Q_{3}$ and subtract this number from $Q_{1}$. $87+24=111$ and $71-24=47$
7. Any number smaller than 47 or larger than 111 would be considered an outlier. Therefore, 36 is the only outlier in this set.

## 统计代写|AP统计辅导AP统计答疑|Modified Boxplots

Modified boxplots are extremely useful in AP Statistics. A modified boxplot is ideal when you are interested in checking a distribution for outliers or skewness, which will be essential in later chapters. To construct a modified boxplot, we use the five-number summary. The box of the modified boxplot consists of $\mathrm{Q} 1, \mathrm{M}$, and $\mathrm{Q} 3$. Outliers are marked as separate points. The tails of the plot consist of either the smallest and largest numbers or the smallest and largest numbers that are not considered outliers by our mathematical criterion discussed earlier. Outliers appear as separate dots or asterisks. Modified boxplots can be constructed with ease using the graphing calculator or computer software. Be sure to use the modified boxplot instead of the regular boxplot, since we are usually interested in knowing if outliers are present. Side-by-side boxplots can be used to make visual comparisons between two or more distributions. Figure $1.4$ displays the test scores from Data Set B. Notice that the test score of 36 (which is an outlier) is represented using a separate point.

Histograms are also useful for displaying distributions when the variable of interest is numeric (Figure 1.5). When the variable is categorical, the graph is called a bar chart or bar graph. The bars of the histogram should be touching and should be of equal width. The heights of the bars represent the frequency or relative frequency. As with modified boxplots, histograms can be easily constructed using the TI-83/84 graphing calculator or computer software. With some minor adjustments to the window of the graphing calculator, we can easily transfer the histogram from calculator to paper. We often use the ZoomStat function of the TI-83/84 graphing calculator to create histograms. ZoomStat will fit the data to the screen of the graphing calculator and often creates bars with non-integer dimensions. In order to create histograms that have integer dimensions, we must make adjustments to the window of the graphing calculator. Once these adjustments have been made, we can then easily copy the calculator histogram onto paper. Histograms are especially useful in finding the shape of a distribution. To find the center of the histogram, as measured by the median, find the line that would divide the histogram into two equal parts. To find the mean of the distributions, locate the balancing point of the histogram.

## 统计代写|AP统计辅导AP统计答疑|Describing Distributions

• 将数据组织成图形显示对于理解统计数据至关重要。本章讨论如何描述用于组织单变量数据的分布和各种类型的图。图表的类型包括修改后的箱线图、直方图、茎叶图、条形图、点图和饼图。AP统计学的学生应该清楚地了解变量是什么以及遇到的变量类型。
• 变量是个体的特征，对于不同的个体可以取不同的值。本章讨论了两类变量：分类变量和定量变量。

• 在描述分布时，描述您在图表中看到的内容很重要。在问题的上下文中解决分布的形状、中心和分布很重要。
• 在描述形状时，请关注分布的主要特征。图形是近似对称的、向左倾斜还是向右倾斜？

## 统计代写|AP统计辅导AP统计答疑|Standard Deviation

s=2.5≈1.5811

• 解决分布中可能存在的任何异常值也很重要。异常值是不属于分布的整体模式的值。能够识别分布中的潜在异常值很重要，但我们还想确定一个值在数学上是否是异常值。
• 示例 4：考虑数据集 B，它由大学统计学课程的考试成绩组成：
98,36,67,85,79,100,88,85,60,69,93,58,65,89,88,71,79,85,73,87, 81,77,76,75,76,73
1. 按升序排列数据。
36,58,60,65,67,69,71,73,73,75,76,76,77,79,79,81,85,85,85,87, 88,88,89,93,98,100求中位数（两个中间数的平均值）： 78 。
2. 求数字前半部分的中位数。这是第一个四分位数，问1:71.
3. 找到数字后半部分的中位数，第三个四分位数，问3:87.
4. 求四分位距 (IQR)：一世问R=问3−问1=87−71=16.
5. 将 IQR 乘以1.5:16×1.5=24.
6. 将此号码添加到问3并从中减去这个数字问1. 87+24=111和71−24=47
7. 任何小于 47 或大于 111 的数字都将被视为异常值。因此，36 是该集合中唯一的异常值。

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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。