### 统计代写|生物统计学作业代写Biostatistics代考| Stem-and-Leaf Diagrams

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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|生物统计学作业代写Biostatistics代考|Stem-and-Leaf Diagrams

A stem-and-leaf diagram is a graphical representation in which the data points are grouped in such a way that we can see the shape of the distribution while retaining the individual values of the data points. This is particularly convenient and useful for smaller data sets. Stem-and-leaf diagrams are similar to frequency tables and histograms, but they also display each and every observation. Data on the weights of children from Example $2.2$ are adopted here to illustrate the construction of this simple device. The weights (in pounds) of 57

called leaves. There are no hard rules about how to construct a stem-and-leaf diagram. Generally, it consists of the following steps:

1. Choose some convenient/conventional numbers to serve as stems. The stems chosen are usually the first one or two digits of individual data points.
2. Reproduce the data graphically by recording the digit or digits following the stems as a leaf on the appropriate stem.

If the final graph is turned on its side, it looks similar to a histogram (Figure $2.10$ ). The device is not practical for use with larger data sets because some stems are too long.

## 统计代写|生物统计学作业代写Biostatistics代考|NUMERICAL METHODS

Although tables and graphs serve useful purposes, there are many situations that require other types of data summarization. What we need in many applications is the ability to summarize data by means of just a few numerical measures, particularly before inferences or generalizations are drawn from the data. Measures for describing the location (or typical value) of a set of measurements and their variation or dispersion are used for these purposes.

First, let us suppose that we have $n$ measurements in a data set; for example, here is a data set:
$${8,2,3,5}$$
with $n=4$. We usually denote these numbers as $x_{i}$ ‘s; thus we have for the example above: $x_{1}=8, x_{2}=2, x_{3}=3$, and $x_{4}=5$. If we add all the $x_{i}$ ‘s in the data set above, we obtain 18 as the sum. This addition process is recorded as
$$\sum x=18$$
where the Greek letter $\Sigma$ is the summation sign. With the summation notation,we are now able to define a number of important summarized measures, starting with the arithmetic average or mean.

## 统计代写|生物统计学作业代写Biostatistics代考|Mean

Given a data set of size $n$,
$$\left{x_{1}, x_{2}, \ldots, x_{n}\right}$$
the mean of the $x$ ‘s will be denoted by $\bar{x}\left(” \mathrm{x}-\mathrm{bar}^{\prime \prime}\right)$ and is computed by summing all the $x$ ‘s and dividing the sum by $n$. Symbolically,
$$\bar{x}=\frac{\sum x}{n}$$
It is important to know that $\Sigma$ (“sigma’) stands for an operation (that of obtaining the sum of the quantities that follow) rather than a quantity itself. For example, considering the data set
$${8,5,4,12,15,5,7}$$
we have
$$\begin{gathered} n=7 \ \sum x=56 \end{gathered}$$
\begin{aligned} \bar{x} &=\frac{56}{7} \ &=8 \end{aligned}
Occasionally, data, especially secondhand data, are presented in the grouped form of a frequency table. In these cases, the mean $\bar{x}$ can be approximated using the formula
$$\bar{x} \simeq \frac{\sum(f m)}{n}$$
where $f$ denotes the frequency (i.e., the number of observations in an interval), $m$ the interval midpoint, and the summation is across the intervals. The midpoint for an interval is obtained by calculating the average of the interval lower true boundary and the upper true boundary. For example, if the first three

intervals are
\begin{aligned} &10-19 \ &20-29 \ &30-39 \end{aligned}
the midpoint for the first interval is
$$\frac{9.5+19.5}{2}=14.5$$
and for the second interval is
$$\frac{19.5+29.5}{2}=24.5$$
This process for calculation of the mean $\bar{x}$ using Table $2.3$ is illustrated in Table 2.7.
\begin{aligned} \bar{x} & \simeq \frac{2086.5}{57} \ &=36.6 \mathrm{lb} \end{aligned}

## 统计代写|生物统计学作业代写Biostatistics代考|Stem-and-Leaf Diagrams

1. 选择一些方便/常规的数字作为词干。选择的词干通常是单个数据点的前一位或两位数。
2. 通过将茎后面的一个或多个数字记录为适当茎上的叶子，以图形方式再现数据。

8,2,3,5

∑X=18

## 统计代写|生物统计学作业代写Biostatistics代考|Mean

\left{x_{1}, x_{2}, \ldots, x_{n}\right}\left{x_{1}, x_{2}, \ldots, x_{n}\right}

X¯=∑Xn

8,5,4,12,15,5,7

n=7 ∑X=56

X¯=567 =8

X¯≃∑(F米)n

10−19 20−29 30−39

9.5+19.52=14.5

19.5+29.52=24.5

X¯≃2086.557 =36.6lb

## 广义线性模型代考

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## MATLAB代写

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