Section outline

  • lesson content

    A group of boys decided to practice their times for the 400 meters one day after school. Five of the boys on the track team gathered together and all decided to practice. They figured out that the best way to do it was to have each person start in turns. One person would run, then the next and then the next until everyone had run. Carla came too so that she could run the stop watch and record the times.
    ::一组男孩决定放学后每天用400米的时间练习时间。 轨道队的五名男孩聚集在一起,决定练习。 他们发现最好的办法是让每个人轮流开始。 一个人会跑,然后是下一个人,然后是下一个人,直到每个人都跑。 Carla也来了,这样她就可以运行停靠手表记录时间。

    All of the boys ran and at the end of it they asked Carla for the times. Although five boys ran, she had only recorded the scores of three boys.
    ::所有男孩都跑去,最后他们问卡拉几次,尽管五个男孩跑了,但她只记录了三个男孩的分数。

    “Why did you do that?” Marco asked.
    ::“你为什么要这样做?” Marco问。

    “I only recorded the first three to cross the finish line,” Carla explained. “At the race, those will be the three winners.”
    ::Carla解释道 : “ 比赛中, 三位赢家将会是三位赢家。 ”

    “But that isn’t accurate!” Marco explained.
    ::」Marco解释道:

    Who is correct?
    ::谁是正确的?

    In this concept, you will learn to understand survey data .
    ::在这个概念中,你们将学会了解调查数据。

    Surveys
    ::调查调查

    A common tool that people use to gather information is a survey . A survey is a method of gathering information by collecting data on a sample of a larger population . A population can refer to any group about which information is desired. In other words, if you want to know about the opinions of students in your school, then the population is the entire school. The population could be an entire city, country, or even a group of plants, animals, or things.
    ::人们用来收集信息的一个常用工具是调查。调查是一种通过收集较大人口抽样数据收集信息的方法。人口可以指任何需要信息的群体。换句话说,如果你想了解学校学生的意见,那么人口就是整个学校。人口可以是整个城市、国家,甚至可能是植物、动物或植物群体。

    As you can imagine, a population can be very large. For this reason, it is oftentimes impractical or even impossible to get information on every single member of the population. In order to save time and resources, you may survey only a small percentage of the population. In order to make sure that the information you gather from a smaller percentage is representative of the entire population, you use techniques to choose the members that you survey. When surveys are carried out appropriately, the information that they tell you can be very useful.
    ::可以想象,人口可能非常庞大。因此,往往不切实际,甚至不可能获得关于每个人口成员的信息。为了节省时间和资源,你只能调查一小部分人口。为了确保你从较小比例收集的信息能够代表整个人口,你使用技术选择你调查的成员。在适当开展调查时,他们告诉你的信息非常有用。

    Let’s think about the different types of samples that can be collected. 
    ::让我们想想可以收集的不同种类的样本。

    Random Sampling
    ::随机抽样

    Monica can take a random sample by giving each student in the school an equal opportunity of being chosen. Like a lottery machine that uses ping pong balls to choose winning numbers, Monica would have to select students completely randomly. For example, if she had a list of students, she could mix up the names and choose the first 50 with her eyes closed.
    ::莫妮卡可以随机抽样,让学校每个学生都有被选中的同等机会。 像彩票机那样使用乒乓球来选择获胜人数,莫妮卡必须完全随机地选择学生。 比如,如果她有学生名单,她可以把名字混在一起,用闭眼来选择前50名。

    Stratified Random
    ::批分随机随机

    In this method, Monica would make sure that she selected an equal number of students from certain strata. Strata are different layers or levels. In her school, students are in levels by grade. In this case, strata can also refer to gender and educational program. If she randomly chooses 25 girls and 25 boys, she is using a stratified random method.
    ::在这种方法中,Monica会确保她从某些阶层中选择同等数量的学生。Strata是不同的层次或层次。在她的学校里,学生是按年级排列的。在这种情况下,阶层也可以提到性别和教育方案。如果她随机选择25名女孩和25名男孩,她就会使用分层随机方法。

    Systematic Sampling
    ::系统抽样

    Monica may also decide to sample students in a systematic manner. That is, she could stand at the front of the school or in the lunch line and sample every 20 th student. This way, she would get approximately 50 students, assuming that they all attend school on the given day and they all come through the same door or go to lunch. If they do not, then she may not get a representative sample ; the sample would be biased .
    ::Monica也可以系统地决定对学生进行抽样。也就是说,她可以站在学校的前面或午餐线上,每20名学生就做一次抽样。 这样,她就会得到大约50名学生,假设他们都在同一天上学,而且他们都从同一个门进来或者去吃午餐。如果他们不这样做,她可能得不到具有代表性的样本;样本就会有偏差。

    Convenience Sampling
    ::便利性抽样

    If Monica finds these methods too difficult, she could go with an easier route and ask the first 50 students that walk by her homeroom, for example. This is called convenience sampling; it is the method that is easiest because it selects the members of the population to whom the sampler has the most access. The problem is that this method does not ensure a representative portion of the entire population. If she is in advanced biology, for example, and asks only students in that room or only students who walk by that room, they may have different views than students in the rest of the school. Perhaps the fact that they share a class or grade level with her will make them more likely to vote for her. That may not be true of the rest of the school.
    ::如果Monica发现这些方法太困难,她可以走比较容易的路线,去问最初的50名学生,他们走在自己的教室,例如,这称为便利抽样;这是最容易的方法,因为抽取的是抽样者最能接触到的人群;问题是,这种方法不能保证整个人口的代表性;例如,如果她从事高级生物学工作,只要求该房间的学生或只有经过该房间的学生,他们的意见可能与学校其他学校的学生不同。也许,他们同她共用一个班级或年级,会使他们更可能投票支持她。这对学校的其余部分来说可能并非如此。

    Self-Selected
    ::自选自选

    There are many people who like to be asked. They like that their opinion counts, they like to express their points-of-view, they like to participate, they like to help, or they like to influence an outcome. If Monica walks around with a sign that says, “Tell me how you feel about homework,” she allows members of the population to select themselves. You may have seen taste-tests in local malls, for example, that have signs reading: “Choose your favorite soda.” People who participate are self-selecting. As with convenience sampling, this may not be a representative portion of the population. People who do not select to participate may have different views from those that do participate.
    ::有许多人喜欢被询问。他们喜欢自己的观点计数,喜欢表达自己的观点,喜欢参与,喜欢帮助,或喜欢影响结果。如果莫妮卡走来走去,留下一个牌子说 : “ 告诉我你对功课的感觉如何 , ” 她允许民众选择自己。 比如,你可能看到当地购物中心的品味测试,这些牌子写着 : “ 选择你最喜欢的苏打水 ” 。 参加的人是自我选择的。 与方便抽样一样,这也许不是人口中的代表性部分。 不选择参加的人可能与参加的人有不同的观点。

    Let’s look at an example.
    ::让我们举个例子。

    There are 2000 students in Monica’s school. She wants to do a survey about student’s opinion on the new homework policy. She knows that she cannot ask everyone. She’ll have to take a sample, a small part of the population, and assume that the information they give her is true for the rest of the school. She plans to ask 50 people. In order to choose the 50 people that she asks, she can use a variety of methods.
    ::莫妮卡的学校里有2000名学生。她想对学生对新家庭作业政策的看法进行调查。她知道她不能向所有人提出询问。她必须抽取样本,占人口一小部分,并假定学校其余部分的情况属实。她打算问50人。为了选择她要求的50人,她可以使用各种方法。

    When a survey is complete, there is still a lot of work to do. After collecting the data, it must be analyzed using a great many choices of displays and statistical measures. From these data analyses, you hope to make some generalizations about the population at large. You also hope, at times, to make decisions based on the data.
    ::当调查完成后,仍有大量工作要做。在收集数据后,必须使用大量的显示和统计计量方法来分析。从这些数据分析中,您希望对广大民众进行一些概括。您还希望有时根据数据做出决定。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about  Carla running the stop watch and recording the times. She only recorded the first three to cross the finish line of the 400 meter race. Marco said she was not accurate as the runners all started at different times.
    ::早些时候,有人给了你卡拉一个问题 卡拉运行停手表和记录时间。她只记录了前三步 跨越400米赛程的终点线。马可说她不准确,因为赛跑者都是在不同的时间开始的。

    Marco is right. The boys all started at a different time. Therefore, the order that they crossed the finish line does not help in determining who was fastest. You have to calculate each time to figure this out. Time, not order, is what makes the difference here.
    ::Marco是对的。男孩们都是在不同的时间开始的。 因此, 他们跨过终点线的顺序无法帮助确定谁是最快的。 您必须每次计算算出这一点。 时间, 而不是顺序, 是这里的区别所在 。

    Example 2
    ::例2

    A number of children were surveyed about the amount of time that they watch TV and the amount of time that they spend studying. The study was completed at a charter school that specializes in college preparation for first- generation Americans. Three students from each class were randomly chosen to participate in the survey. Their results are shown in the table below:
    ::对一些儿童进行了调查,了解他们看电视的时间和学习的时间,研究是在一所专门为第一代美国人准备大学的特许学校完成的,每个班有三名学生被随机挑选参加调查,结果见下表:

    TV 3.5 3.5 3.5 5 3 1 1 0 0
    Studying 2 1.5 2.5 1 3.5 4.5 5 5 1
    TV 1 2 2 2 1.5 0 0.5 4 4
    Studying 3.5 7 6 5.5 5 6 4 0.5 1
    TV 4 6 3 4 3 6 6.5 1 1
    Studying 1.5 1 4 2 4.5 0 0.5 7 1

    The following conclusions were made.
    ::得出了以下结论。

    1. Montoya Charter School students who watch more than 2 hours of TV do not study.
      ::蒙托亚特许学校学生,如果看两小时以上的电视,则不学习。
    2. Children in the United States watch too much TV.
      ::美国儿童看太多电视了。
    3. Students who do not study enough will get low grades.
      ::学习程度不够的学生将获得低年级。
    4. TV is causing students to be less interested in school.
      ::电视使学生对学校的兴趣降低。

    Draw a scatterplot to visually display this data. Analyze the conclusions that were made.
    ::绘制一个散射图以直观显示此数据。 分析得出的结论 。

    First, draw the scatterplot. Clearly, this data is difficult to interpret in this form. Because the school is looking for a relationship between TV time and studying time, a scatterplot is an excellent display of the data.
    ::首先, 绘制散射图 。 显然, 此数据很难以这种形式解释 。 因为学校正在寻找电视时间和学习时间之间的关系, 散射图是极好的数据显示 。

    lesson content

    Next, analyze the conclusions that were made.
    ::接下来,分析得出的结论。

    1. Montoya Charter School students who watch more than 2 hours of TV do not study.
    ::1. 蒙托亚特许学校学生如果观看两小时以上的电视,不学习。

    The data shows that many students who watch more than 2 hours of TV do study although generally fewer hours.
    ::数据显示,许多观看电视两小时以上的学生确实在学习,尽管通常时间较少。

    2. Children in the United States watch too much TV.
    ::2. 美国儿童看太多电视。

    This sample was only taken at a charter school that serves a specific population. You cannot generalize this data to other populations, like the entire United States.
    ::这个样本只是在一个为特定人口服务的包租学校里采集的。你不能将这些数据推广到其他人口,比如整个美国。

    3. Students who do not study enough will get low grades.
    ::3. 学习程度不够的学生将获得低年级。

    There is no data in this study that relates studying time to grades.
    ::这项研究没有关于学习时间与年级有关的数据。

    4. TV is causing students to be less interested in school.
    ::4. 电视使学生对学校不太感兴趣。

    A scatterplot does not imply causation, only correlation ; the variables are shown to have a negative relation- ship, but that does not mean that one causes the other. If you take television time away from students, it does not mean that they will necessarily study more nor be more interested in school.
    ::散射图并不意味着因果关系,而只是相关关系;变量显示存在负面关系 — — 船舶,但这并不意味着其中一方造成另一方。 如果你把电视时间从学生身上抽走,这并不意味着他们一定会学习更多,也不会对学校更感兴趣。

    Example 3
    ::例3

    Five students were surveyed in each of the seventh grade homerooms. What type of sampling method is this?
    ::在七年级每间教室对五名学生进行了调查,这是哪种抽样方法?

    The answer is a stratified random sample.
    ::答案是分层随机抽样。

    Example 4
    ::例4

    At a concert, the twentieth person in each of eight lines was asked about how he/she purchased his/her ticket. What type of sampling method is this?
    ::在一次音乐会上,八行各行的第二十人被问及他/她是如何购买机票的,这是哪种抽样方法?

    The answer is a systematic sampling method.
    ::答案是一种系统的取样方法。

    Example 5
    ::例5

    At a football game, only the people who agreed to be surveyed were surveyed. What type of sampling method is this?
    ::在一场足球比赛中,只调查同意接受调查的人。这是哪种抽样方法?

    The answer is a self- selected sampling method.
    ::答案是自选抽样方法。

    Review
    ::回顾

    Define each of the following terms.
    ::界定以下每一术语。

    1. Survey
    ::1. 调查

    2. Random sample
    ::2. 随机抽样

    3. Stratified sample
    ::3. 分层抽样

    4. Systematic sample
    ::4. 系统抽样

    5. Convenience sample
    ::5. 便利抽样

    6. Self-Selected sample
    ::6. 自选样本

    Name each sampling method described below.
    ::列出下列每种取样方法。

    7. A mother asks everyone in her office-building about the best restaurant in town.
    ::7. 一位母亲向她的办公楼里的每个人询问了城里最好的餐厅。

    8. A police traffic stop pulls over every 3rd car to check for proper insurance.
    ::8. 警察的交通阻塞车停在每三辆车上,检查是否有适当的保险。

    9. A phone company uses a computer to choose customer for a satisfaction survey. 5% of each region are chosen randomly.
    ::9. 电话公司使用计算机选择客户进行满意度调查。 每个区域的5%是随机选择的。

    10. People call a phone number given on a receipt at a restaurant to answer questions about cleanliness and service. Each person who calls gets entered into a drawing.
    ::10. 人们在餐馆的收据上打一个电话号码,回答关于清洁和服务的问题,每个打电话的人都画上图。

    11. A cattle herder checks for Mad Cow Disease by drawing blood from 30 cows that he chose by drawing their ID numbers from a hat.
    ::11. 牧牛人通过抽取他选择的30头奶牛的血来检查麦地牛病,从帽子上提取他们的身份证号码。

    12. Every fifth person to buy gasoline is asked about their automobile.
    ::12. 购买汽油的五分之一的人都会被问及他们的汽车。

    13. An announcement for a survey is mentioned at a movie theater. Anyone who chooses to participate can.
    ::13. 在电影院提到宣布进行调查,任何选择参加的人都可以参加。

    14. Every fifth grader at Smith School is asked about the number of hours he/she watches television per week.
    ::14. 史密斯学校每五年一个年级的学生被问及每周看电视的小时数。

    15. A computer calls people from the phone book and asks them about their political choices.
    ::15. 一台计算机从电话簿上给人们打电话,询问他们的政治选择。

    Review (Answers)
    ::回顾(答复)

    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 。