12.1 感减理由

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  扣减和扣减理由

  

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  Suppose you were given the task of collecting data from each class in your school on the ratio between male and female students. After reviewing the M:F ratios of each classroom, would you use inductive reasoning or to come up with a hypothesis regarding an average M:F ratio for the school? What kind of reasoning would be involved if your friend asked you to review your data to see if her theory about ratios being different in different grades was supported by your observations?
  ::假设你被赋予从学校每个班级收集男女学生比例数据的任务。 在审查每个班级的M:F比率后,你是否使用感性推理,或者对学校的平均M:F比率提出假设?如果你的朋友要求你审查你的数据,看她关于不同年级比例的理论是否得到你观察的支持,那么你将涉及什么样的推理呢?

  

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  Inductive and Deductive Reasoning 
  ::扣减和扣减理由

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  One of the primary uses of probability and statistics is to learn about parameters of a population, and to do that, one must be able to reason from a sample to a population. Either a person observes something and tries to explain it by collecting and distilling data into a conclusion , or else he/she begins with a hypothesis and seeks data to support or renounce it. In this lesson, we will discuss these two types of reasoning, Inductive and Deductive.
  ::概率和统计数据的主要用途之一是了解人口参数,为此,人们必须能够从抽样中向人口解释。 一个人要么观察某事,试图通过收集和提炼数据来解释它,要么从假设开始,寻求数据支持或放弃它。 在这个教训中,我们将讨论这两类推理,即诱导和贬损。

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  • Deductive Reasoning – Begins with the question or theory and works toward specific examples or evidences to support or renounce it.
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    • Every morning, I eat eggs for breakfast. Every day, I am not hungry again until lunchtime. This morning if I eat eggs for breakfast, I will not be hungry until lunchtime.
      ::每天早上,我吃鸡蛋做早餐;每天,直到午餐时间,我都不饿。 今天早上,如果我吃鸡蛋做早餐,我直到午餐时间才饿。
    
    ::贬义的理由 — — 从问题或理论开始,并努力寻找支持或放弃它的具体例子或证据。 每天早上,我吃鸡蛋做早餐。 每天,直到午餐时间,我都不饿。 今天早上,如果我吃鸡蛋做早餐,我直到午餐时间才饿。
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  • Inductive Reasoning – Begins with specific observations or data and works toward a general statement to explain it.
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    • This morning I ate eggs for breakfast and was not hungry until lunchtime. As long as I eat eggs for breakfast, I’ll never be hungry until lunchtime.
      ::今天早上我吃鸡蛋做早餐,直到午餐时才饿。 只要我吃鸡蛋做早餐,直到午餐时才饿。
    
    ::入门理性 — — 从具体的观察或数据开始,并致力于做出一般性解释。 今天上午我吃了鸡蛋做早餐,直到午餐才饿。 只要我吃鸡蛋做早餐,直到午餐才饿。

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  In scientific study, both sorts of reasoning are used, often in conjunction and to support each other. However, as you will see over the next few lessons, there are a lot of ways to make errors in reasoning (called fallacies ), and knowing what type of reasoning you are using will help you to learn which fallacies to watch out for!
  ::在科学研究中,这两种推理都使用,往往结合使用,并相互支持。然而,正如你们在接下来的几个教训中看到的那样,在推理中有很多方法可以犯错误(所谓的谬误 ) , 知道你们使用的推理类型会帮助你们了解哪些谬误值得注意!

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  Choosing the Applicable Reasoning 
  ::选择适用的理由

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  1. What sort of reasoning is applicable to finding the solution to a five-step linear equation such as the one below?
  ::1. 对于以下五步线性等式的解决方案,应适用何种推理?

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  $$\begin{align*}2(x+3)-7 &= x+4 \\ 2(x+3) &= x+11 \\ 2x+6 &= 11 \\ 2x-x &= 11-6 \\ x &= 5\end{align*}$$
  ::2(x+3)-7=x+42(x+3)=x+112x+6=112x-x=11-6x=5

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  This is deductive reasoning, since we started with a statement or theory:  $\begin{align*}2(x+3)-7=x+4\end{align*}$ , and used a step-by-step process to find a specific example supporting it, namely that if $\begin{align*}x=5\end{align*}$ , then $\begin{align*}2(5+3)-7=5+4\end{align*}$ , so the original statement is supported by a specific example.
  ::这是一种推理推理,因为我们从一个陈述或理论(2(x+3)-7=x+4)开始,并使用一个逐步过程来找到一个支持它的具体例子,即如果 x=5,那么如果2(5+3)-7=5+4,那么原来的陈述就得到一个具体例子的支持。

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  Since we progressed from general to specific, this was deductive reasoning.
  ::自从我们从一般发展到具体以来,这是推理推理。

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  2. Assuming the sequence below, what type of reasoning would you use to conjecture the next number in the sequence?
  ::2. 假设以下顺序,你用哪种推理来猜测序列中的下一个序号?

  $$\begin{align*}1, 4, 10, 19, 31, 46, 64, \ldots\end{align*}$$

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  This is an example of inductive reasoning, since we started with a number of specific observations, namely the 1 ^st , 2 ^nd , 3 ^rd , 4 ^th , and so on numbers in a sequence, and use the observations to make the statement that the pattern is to add $\begin{align*}3n\end{align*}$ , where  $\begin{align*}n\end{align*}$ is the count, to each number to get the next: $\begin{align*}1 + 3(1) = 4, \ 4+3(2) = 10, \ 10 + 3(3) = 19, \ 19 + 3(4) = 31\end{align*}$ , and so on. That tells us that the next number in the series should be:  $\begin{align*}64 + 3(7) = 85\end{align*}$ .
  ::这是感性推理的一个实例,因为我们首先从一系列具体观察开始,即第1、第2、第3、第4等次关于数字的观察,并用观察来说明,模式是在每个数字中增加3n,n是n,以获得下一个数字:1+3(1)=4,4+3(2)=10,10+3(3)=19,19+3(4)=31,等等。这告诉我们,系列中的下一个数字应该是:64+3(7)=85。

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  Since we progressed from specific to general, this was inductive reasoning.
  ::自从我们从具体发展到一般以来,这是引人入胜的推理。

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  Determining What Type of Reasoning is Expressed
  ::确定何种理由说明类型

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  What sort of reasoning is expressed in the following statements?
  ::以下陈述中表述了何种推理?

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  Chloe took her umbrella to work today, and it rained.
  ::克洛伊今天带着她的伞去工作 下雨了

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  Every time Chloe takes her umbrella, it will rain.
  ::克洛伊每次拿起伞 都会下雨

  

  :

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  This is inductive reasoning, beginning with the specific statement about a specific day and action, and progressing to a general statement about all days with the same action.
  ::这是一种启发性推理,首先是具体陈述具体日期和行动,然后以同样的行动逐天进行一般性陈述。

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  Earlier Problem Revisited
  ::重审先前的问题

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  Suppose you were given the task of collecting data from each class in your school on the ratio between male and female students. After reviewing the M :F ratios of each classroom, would you use inductive reasoning or deductive reasoning to come up with a hypothesis regarding an average M:F ratio for the school? What kind of reasoning would be involved if your friend asked you to review your data to see if her theory about ratios being different in different grades was supported by your observations?
  ::假设你被赋予了从学校每个班级收集男女学生比例数据的任务。 在审查每个教室的M:Fratios之后,你是否会用感性推理或推理来提出有关学校平均M:F比例的假设?如果你的朋友要求你审查你的数据,看她关于不同年级比例的理论是否得到你观察的支持,那又会涉及什么样的推理呢?

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  First, you begin with specific examples of the ratios of males and females and use them to create a general statement about the ratio of the entire school. That was inductive reasoning: specific to general. Second, you started with the general statement that the ratios are different in different grades, and considered the specific data to support or not support the statement. That was deductive reasoning: general to specific.
  ::首先,你首先举出男女比例的具体例子,然后用这些例子来就整个学校的比例作出一般性说明。这是个引人入胜的推理:具体针对一般情况。第二,你首先提出一般性说明,即不同年级的比例不同,并审议了支持或不支持该说明的具体数据。这是推理:一般针对具体情况。

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  Examples 
  ::实例

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  For Examples 1-4, describe the type of reasoning demonstrated in each passage.
  ::关于例1-4,请说明每一段落所显示的推理类型。

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  Example 1
  ::例1

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  Scott leaves for school at 8:15 in the morning every day, it takes him 15 minutes to get to school, and he arrives on time. If Scott leaves at 8:15 this morning, he will arrive at school on time.
  ::斯科特每天早上8点15分离开学校,他要15分钟才能上学,他准时到达。如果斯科特早上8点15分离开,他将准时到达学校。

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  This is deductive reasoning, starting with a general statement about Scott's actions everyday and progressing to the specific occurrence of today.
  ::这是推理推理,首先从关于斯科特每天行动的一般性陈述开始,然后到今天的具体发生。

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  Example 2
  ::例2

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  On Monday, Sophie went to lunch at the local fast-food joint on her lunch break and arrived back at school in time for class. On Tuesday, she did the same thing and was on time again. If Sophie goes to the same fast-food place for lunch on every day, she will be back in time for class.
  ::周一,Sophie在午餐休息时到当地快餐店吃午餐,并准时回到学校上课。星期二,她也做了同样的事情,而且又在上课。如果Sophie每天去同一个快餐店吃午餐,她就会准时回来上课。

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  This is inductive reasoning, starting with specific examples of actions and progressing to a general statement about every similar action. 
  ::这是引人入胜的推理,首先是具体的行动例子,并逐步形成关于每一项类似行动的一般性说明。

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  Example 3
  ::例3

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  $\begin{align*}3(x-4)-7=6x\end{align*}$ , therefore, $\begin{align*}x=-6.3 \overline{3}\end{align*}$ .
  ::3 (x-4)- 7=6x, 因此x 6.33'.

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  Deductive reasoning, from a general statement to a specific example of the statement being true.
  ::从一般性发言到具体例子说明声明属实,推理不合理。

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  Example 4
  ::例4

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  If $\begin{align*}y=7\end{align*}$ , and $\begin{align*}x = 4\end{align*}$ , therefore $\begin{align*}x \times \frac{7}{4} = y\end{align*}$ .
  ::如果y=7、x=4,则xxx74=y。

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  Inductive reasoning, from specific stated values of  $\begin{align*}x\end{align*}$ and  $\begin{align*}y\end{align*}$ to a general statement about them both.
  ::推论,从x和y的具体明确价值到关于两者的一般性说明。

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  Review 
  ::回顾

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  For each question, state whether the reasoning is an example of inductive or deductive logic.
  ::对于每个问题,请说明推理是推理或推理逻辑的例子。

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  1. All housecats are felines. All felines have claws. Therefore all housecats have claws.
     ::所有的家庭猫都是猫头鹰,所有的家庭猫都有爪子,所以所有的家庭猫都有爪子。
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  2. My dog has fleas. My neighbor’s dog has fleas. Therefore all dogs must have fleas.
     ::我的狗有跳蚤,我的邻居的狗有跳蚤,因此所有狗都必须有跳蚤。
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  3. All cows like hay. My cow will like hay.
     ::所有牛都喜欢干草 我的牛都喜欢干草
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  4. My Mac laptop is fast. All Mac laptops are fast.
     ::我的麦克笔记本电脑速度很快 所有的麦克笔记本电脑速度很快
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  5. My tennis shoes are comfortable. My friend’s tennis shoes are comfortable. All tennis shoes are comfortable.
     ::我的网球鞋比较舒服,我朋友的网球鞋比较舒服,所有网球鞋都比较舒服。
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  6. The scalloped potatoes I took from the oven were cheesy. The enchiladas I took from the oven were cheesy. If I take cookies from the oven, they will be cheesy.
     ::我从烤箱里拿的扇贝土豆很俗气,我从烤箱里拿的菜薯很俗气,如果我从烤箱里拿的饼干,它们就会很俗气。
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  7. Everything cooked on the stove gets hot. If I cook macaroni on the stove, it will get hot.
     ::炉子上煮的东西都热了 如果我在炉子上煮通心粉,它会热的
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  8. iPads are popular. iPhones are popular. Every phone or tablet is popular.
     ::iPads很受欢迎,iPhone很受欢迎,每部电话或平板电脑都很受欢迎。
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  9. Roses are red. Tomatoes are red. All red things come from plants.
     ::玫瑰是红的 番茄是红的 所有红的都来自植物
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  10. Rock music is loud. Sayber listens to rock music. Sayber’s music is loud.
      ::摇滚音乐响亮。 赛伯听摇滚音乐。 赛伯的音乐响亮。
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  11. Milk is good with cookies. Snicker doodles are cookies. Milk is good with snicker doodles.
      ::牛奶很好吃饼干 饼干是饼干 牛奶很好吃饼干
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  12. Hummers use a lot of gas. Suburbans use a lot of gas. Large SUV’s use a lot of gas.
      ::悍马车使用大量的天然气。 郊区使用大量的天然气。 大SUV使用大量的天然气。
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  13. My garden has pumpkins. My dad’s garden has pumpkins. All gardens have pumpkins.
      ::我的花园有南瓜,我爸爸的花园有南瓜,所有花园都有南瓜。
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  14. Prob and Stats students are smart. You are a Prob and Stats student. You are smart.
      ::Prob和Stat学生都很聪明,你是Prob和Stat学生,你很聪明
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  15. Students who study hard get good grades. You are a student who studies hard. You will get good grades.
      ::学习勤奋的学生获得好成绩。您是学习勤奋的学生。您将获得好成绩。

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。