章节大纲

  • 常规

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  • 按数据类型显示

    lesson content

    Ahmed conducted a survey of the favorite kind of breakfast cereal for 8th graders. He organized his survey results into the table below. 
    ::艾哈迈德对八年级学生最喜欢的早餐谷类进行了调查,并将调查结果列入下表。

    Favorite Cereal

    Cereal
    ::谷物

    Amount of Students
    ::学生人数

    Fruit Flakes
    ::果果花

    12

    Chocolate Puffs
    ::巧克力泡泡巧克力

    18

    Oat-O’s
    ::Oat-O ' Oat-O ' Oat-O '

    9

    Raisin Delight
    ::葡萄灯光

    3

    Honey Crunch
    ::蜂蜜库

    17

    Bran Loops
    ::Bran 循环

    3

    Oat Squares
    ::Oat 广场

    9

    Fiber Max
    ::自由马克思

    2

    Fruities
    ::果果

    10

    Cinnamon Squares
    ::肉桂广场

    17

    How can Ahmed display his survey data ? What can Ahmed say about the kind of breakfast cereal that 8th graders like? 
    ::Ahmed怎么能展示他的调查数据呢? Ahmed对八年级学生喜欢的早餐麦片有什么看法?

    In this concept, you will learn how to create a survey, determine the best sample sizes based on populations, and understand the influence of bias . 
    ::在这个概念中,你将学会如何建立调查,根据人口确定最佳抽样规模,并了解偏见的影响。

    Displaying by Type of Data
    ::按数据类型显示

    Data is a set of numerical or non-numerical information. Data can be collected and analyzed in many different ways. In this concept you will consider ways of collecting both numeric and non-numeric data.
    ::数据是一组数字信息或非数字信息。数据可以多种不同方式收集和分析。在这个概念中,你会考虑收集数字数据和非数字数据的方法。

    A survey is one way to collect information about a population , or group of people. Surveys can collect information in a number of different ways, such as asking questions, measuring something, or counting the frequency or occurrence of something.
    ::调查是收集人口或人群信息的一种方式。 调查可以多种不同方式收集信息,例如提问、测量某事或计算某事的频率或发生频率。

    A population  is a group of people that share similar characteristics.
    ::人口是一个具有类似特征的群体。

    A sample  is the group of people that are surveyed. A sample is a subset, or small group, of the total population. Surveys are conducted on samples because populations are normally too big to survey. 
    ::抽样是接受调查的人群群体,抽样是总人口的一个子集或小群体,对抽样进行调查,因为人口通常太大,无法调查。

    A random sample  is a group of people who have been randomly selected to survey. This means that every person in the population has an equal chance of being asked to participate in the survey. 
    ::随机抽样是随机挑选的一组调查对象,这意味着人口中的每个人都有被要求参加调查的同等机会。

    Bias  refers to a feeling or prejudice towards something. When conducting a survey using questions, it is important that the questions are unbiased. Good survey questions are short and concise and usually begin with “Who," "What," "When," "Where," "Why," or "How.”
    ::Bias 指的是对某事物的一种感觉或偏见。 在使用问题进行调查时,问题必须是不带偏见的。 良好的调查问题简明扼要,通常从“谁 ” 、 “什么 ” 、 “何时 ” 、 “哪里 ” 、 “为什么 ” 或“如何 ” 开始。

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

    Hollywood Middle School is holding elections for the student body president. Create a survey that will predict the winner of the election. 
    ::好莱坞中学正在举行学生会主席的选举。

    First, determine the question that will be asked on the survey. Good survey questions are short and concise and usually begin with “Who," "What," "When," "Where," "Why," or "How.” For this survey, one question is enough. Since the survey should predict the winner, the survey question should be "Who will you vote for student body president?"
    ::首先,确定调查中要问的问题。 良好的调查问题是简短和简洁的,通常从“谁 ” 、 “什么 ” 、 “什么 ” 、 “什么时候 ” 、 “哪里 ” 、 “为什么 ” 或“如何 ” 开始。 对于这次调查来说,一个问题就足够了。既然调查应该预测获胜者,那么调查问题应该是“你将投票给学生会主席谁? ”

    Next, determine the population and sample. The population for this survey is all students at Hollywood Middle School who can vote in the election. The sample should be randomly selected students who are in the population. The larger number of students surveyed, the greater reliability the survey results have. 
    ::接下来,决定人口和抽样。本次调查的人口是所有好莱坞中学学生,他们都可以在选举中投票。抽样应该是随机挑选的人口中的学生。接受调查的学生越多,调查结果就越可靠。

    The answer is the survey should ask the question "Who will you vote for student body president?" The survey should be asked of randomly selected Hollywood Middle School students who are able to vote. The survey should be conducted at school, where there is an equal chance of participating in the survey. 
    ::答案是调查应该问一个问题:“你将投票给学生会主席谁? ”调查应该问随机挑选的好莱坞中学生,他们可以投票。调查应该在学校进行,在学校有同等机会参加调查。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Ahmed, who conducted a survey of 8th graders favorite kind of breakfast cereal.
    ::早些时候,你被问及 Ahmed的事, 他对八年级学生们 喜欢的早餐麦片进行了调查。

    He organized his data in the table below. 
    ::他在下表中整理了他的数据。

    Favorite Cereal
    Cereal Amount
    Fruit Flakes 12
    Chocolate Puffs 18
    Oat-O’s 9
    Raisin Delight 3
    Honey Crunch 17
    Bran Loops 3
    Oat Squares 9
    Fiber Max 2
    Fruities 10
    Cinnamon Squares 17

    Ahmed wants to display his survey data, but doesn't know how.
    ::Ahmed想展示他的调查数据 但不知道如何

    How can Ahmed display his survey data? What can Ahmed say about the kind of breakfast cereal that 8th graders like? 
    ::Ahmed怎么能展示他的调查数据呢? Ahmed对八年级学生喜欢的早餐麦片有什么看法?

    First, consider what type of data Ahmed is trying to display. In this case, the data are numerical values that represent an amount for ten different categories.
    ::首先, 请考虑 Ahmed 想要显示的数据类型。 在此情况下, 数据是数值, 代表十个不同类别的数值 。

    Next, consider if Ahmed's data is best shown graphically? In Ahmed's case, his data is best represented graphically. 
    ::接下来,考虑一下Ahmed的数据是否最好用图形显示?在Ahmed的案例中,他的数据最好用图形表示。

    Next, since the data compares the number of people who like a given cereal, a bar graph is best.   
    ::其次,由于数据比较了喜欢特定谷物的人数,因此最好用条形图来比较。

    To create a bar graph, first draw the horizontal (x) and vertical 是的 axes. 
    ::要创建条形图,请先绘制水平(x)和垂直是的轴。

    Next, label the horizontal axis. The horizontal axis lists the different kinds of cereal. In this case, the category will be "Cereal."  
    ::下一步, 标记水平轴。 水平轴列出不同种类的谷物。 在这种情况下, 类别将是“ 谷物 ” 。

    Next, label the vertical axis. The vertical axis lists the amount of people who like each cereal. In this case, the category will be "Amount."
    ::接下来标出垂直轴。 垂直轴列出喜欢每份谷物的人的数量。 在这种情况下, 类别将是“ 数量 ” 。

    Next, title the graph. The title of the graph should be short and clear. It should explain what data is presented in the graph. In this case, the title will be “Favorite Cereal Survey.”
    ::下个标题是图表。 图表的标题应该简短清晰。 它应该解释图表中显示的数据。 在这种情况下, 标题将是“ 最喜爱的谷物调查 ” 。

    Then, determine the units on the vertical axis. To do this, start by reviewing the smallest and largest values in the table. The smallest value is 2 and the largest is 18. Based on these values label the vertical axis from 0-20 by a unit of 2. Therefore, the vertical axis will start at 0 and go to 20 by increments of 2.
    ::然后确定垂直轴上的单位。 为此, 首先从审查表中最小和最大的值开始。 最小值为 2, 最大值为 18 。 基于这些值, 0-20 的垂直轴标为 2 的单位为 2 。 因此, 垂直轴将从 0 开始, 以 2 递增为 20 。

    Next, draw the vertical columns. To do this, write each cereal along the horizontal axis. Be sure to leave space between each one. Then draw the column vertically until it reaches the quantity for that activity. For example, draw a vertical column to the number “12” for the cereal “Fruit Flakes.”
    ::接下来绘制垂直列。 要做到这一点, 请在水平轴上写下每张谷物。 请确定在每张之间留下间距 。 然后垂直绘制列, 直至达到该活动的数量 。 例如, 绘制一个垂直列, 直到谷类“ Froit Flakes” 的“ 12” 数字 。

    Next, analyze the bar graph to draw conclusions about the cereal preferences of 8th graders. 
    ::接下来,分析条形图 以得出关于八年级学生的 谷类偏好的结论。

    The first answer is the graph should look like the one below. The second answer is: the favorite cereal among 8th graders is Chocolate Puffs; the least favorite cereal is Fiber Max; and Honey Crunch and Cinnamon Squares are the second favorite cereals of 8th graders. 
    ::第一个答案是图表应该像下图一样。第二个答案是:8年级学生中最喜欢的谷类是巧克力泡芙;最不喜欢的谷类是Fiber Max;蜂蜜Crunch和Cinnamon广场是8年级学生第二喜欢的谷类。

    lesson content

    Example 2
    ::例2

    Miranda creates a survey to determine what sport 7th graders prefer to play in gym class. She asked her friends on the soccer team, "Is your favorite sport to play in gym class soccer?" Explain why Miranda's survey is unreliable and how she can improve its reliability. 
    ::米兰达创建了一个调查来确定七年级学生喜欢在体育课上玩什么运动。她问足球队的朋友,“你最喜欢在体育课足球中玩运动吗?” 解释为什么米兰达的调查不可靠,以及她如何提高调查的可靠性。

    First, consider the question Miranda asked on her survey. Is her question a good survey question? Is the question unbiased? Good survey questions are short and concise and usually begin with “Who," "What," "When," "Where," "Why," or "How.”
    ::首先,请考虑米兰达在她的调查中提出的问题。她的问题是否是一个很好的调查问题?问题是否公正?好的调查问题是简短和简洁的,通常从“谁”、“什么”、“何时”、“在哪里”、“为什么”或“如何”开始。

    Next, consider Miranda's population and sample. What is Miranda's population? What is her sample? Are the participants in her sample randomly selected? Is her sample unbiased?
    ::接下来,考虑一下米兰达的人口和样本。米兰达的人口是什么?她的样本是什么?她的样本是什么?样本的参与者是随机挑选的吗?她的样本是否不带偏见?

    The answer is Miranda's survey is unreliable because: the survey question and sample are  biased . Miranda should use a good survey question, such as "What is your favorite sport to play in gym class?" Miranda should ask her survey question to a random sample of students, not only her friends on the soccer team. Miranda could ask every other 7th grade student that leaves gym class her survey question. This would ensure a randomly selected and large sample. 
    ::答案是米兰达的调查是不可靠的,因为:调查问题和抽样是有偏向的。米兰达应该使用一个良好的调查问题,比如“你最喜欢在体育课上玩什么运动?”米兰达应该向随机抽样的学生,而不仅仅是足球队中的朋友,询问她的调查问题。米兰达可以询问离开体育课的其他7年级学生她的调查问题。这将确保随机挑选和大量抽样。

    Example 3
    ::例3

    Twenty-five households were asked to participate in a survey in which they were asked to approximate the number of hours they watch T.V. each day. The results of the survey are listed on the table below. Create a display of the data, then determine the percentage of people that watched T.V. between 4-5 hours per day.
    ::25个家庭被要求参加一项调查,调查要求他们每天看T.V.的小时数,调查结果见下表:建立数据显示,然后确定每天看T.V.的人在4至5小时之间的百分比。

    First, determine what is the best kind of display for this data. Since these values are numerical and show the frequency of how much T.V. people watch, a histogram is the best type of display. 
    ::首先, 确定该数据的最佳显示类型。 由于这些值是数字, 并显示 T. V. 人观看的频率, 直方图是最佳显示类型 。

    To create a histogram, first a frequency table must be made. To create a frequency table, first identify the bins , or intervals, which will be the left hand column of the table. The bins in this case will be the amount of time people watch T.V. Next, calculate the frequency, or occurrences, of the bins. This data will be in the right hand column of the table.  
    ::要创建直方图,首先必须绘制一个频率表。要创建频度表,首先要标明文件夹,或间隔,这是表格的左手列。此情况下的文件夹将是人们观看 T.V. 的时间数量。接下来,计算文件夹的频率或发生次数。此数据将放在表格右手列中。

    Time Watching T.V.

    Bins: Hours of Television
    ::Bins:电视时数

    Frequency
    ::频率频率频率

    0 – 1

    5

    2 – 3

    8

    4 – 5

    9

    6 – 7

    3

    Next, create the histogram. To do this, first draw the horizontal (x)  and vertical 是的 axes.
    ::下一步,创建直方图。要做到这一点,首先绘制水平(x)和垂直是的轴。

    Next, label the horizontal axis. The horizontal axis lists the different categories of data. In this case, the category will be "Hours."  
    ::下一步,标签水平轴。水平轴列出数据的不同类别。在此情况下,分类为“小时”。

    Next, label the vertical axis. The vertical axis lists the quantity or amount of the data. In this case, the category will be "Frequency."
    ::下一步,标签垂直轴。垂直轴列出数据的数量或数量。在此情况下,类别为“数量”。

    Next, title the graph. The title of the graph should be short and clear. It should explain what data is presented in the graph. In this case, the title will be “Hours of Television Watched.”
    ::下个标题是图表。 图表的标题应该简短清晰。 它应该解释图表中显示的数据。 在这种情况下, 标题将是“ 监视电视的时间 ” 。

    Then, determine the units on the vertical axis. To do this, start by reviewing the smallest and largest frequencies in the table. The smallest value is 3 and the largest is 9. Based on these values label the vertical axis from 0-10. Since the range is small the vertical axis should use a unit of 2.
    ::然后,确定垂直轴上的单位。要做到这一点,首先审查表格中最小和最大的频率。最小值为3,最大值为9。根据这些值,垂直轴从 0- 10 标记为垂直轴。由于范围小,垂直轴应该使用2 的单位。

    Next, draw the vertical columns. To do this, write each bin along the horizontal axis. Then draw each column vertically until it reaches the frequency for that time. For example, draw a vertical column to the number 1 for the bin 0-2. Continue to draw all the columns and do not leave space between them. 
    ::下一步, 绘制垂直列。 要做到这一点, 请沿着水平轴写下每个文件箱。 然后垂直绘制每个文件箱, 直至它达到该时间的频率。 例如, 将一个垂直列划到文件箱 0-2 的编号 1 上。 继续绘制所有文件箱, 并且不要在它们之间留下空隙 。

    Next, determine the percent of people that watched T.V. between 4-5 hours per day. To do this, divide the number of people who watch between 4-5 hours per day by the total number of people surveyed. Then multiple by 100 to convert the decimal to a percentage.  
    ::其次,确定每天4-5小时观看T.V.的人的百分比。为此,将每天看4-5小时的人数除以接受调查的总人数。然后乘以100将小数点转换为百分比。

    9 ÷ 25 = 0.36

    0.36 × 100 = 36 %

    The answer is the graph should look like the one below and the percent of people that watch between 4-5 hours per day is 36%. 
    ::答案是图表应该像下面的图, 每天4至5小时的观察者占36%。

    lesson content

    Example 4
    ::例4

    A survey will be conducted to determine what activities 6th grade students at Judson Middle School like to do on the weekends. Of the three options below, explain which option is the best way to conduct the survey?  
    ::将进行一项调查,以确定贾德森中学六年级学生周末喜欢从事哪些活动。 在下文的三个选项中,请解释哪个选项是进行调查的最佳方式?

    1. Go to the mall and survey every tenth person that walks by.
      ::去商场调查每10个路过的人
    2. Survey 6th graders at a local movie theater.
      ::调查当地电影院的6年级学生。
    3. Survey every third person leaving each 6th grade class.
      ::每三名离开6年级班的人中,每三名就进行一次调查。

    First, analyze the options to conduct the survey and determine which one will be the least biased. Then determine why the other options are more biased. 
    ::首先,分析开展调查的选项,并确定哪些将是最不偏向的。然后确定为什么其他选项更偏向。

    The answer is the best way to conduct the survey is C. This is the most unbiased approach and ensures that everyone in the population is of equal chance to participate in the survey. A and B are not good options because not every 6th grade student has an equal chance of participating in the survey. Also, those students how are asked at the mall or movie theater are a biased group and may not accurately represent all 5th grade students at Judson. 
    ::调查的最佳方式是C。 这是最公正的方法,确保人口中的每个人都有同等机会参加调查。A和B不是好选择,因为并不是每个六年级学生都有同等机会参加调查。此外,这些学生在商场或电影院中被问到如何是带有偏见的群体,可能不能准确地代表贾德森所有五年级学生。

    Example 5
    ::例5

    Oscar created a survey to find out if 8th grade students liked the lunch served in the cafeteria. He asked the students who brought their lunch, "Is the cafeteria pizza good?" Explain why Oscar's survey is unreliable and how he can improve its reliability. 
    ::奥斯卡创建了一个调查,以了解八年级学生是否喜欢在餐厅提供的午餐。他问带午餐的学生们,“餐厅比萨饼好吃吗? ”解释奥斯卡的调查为什么不可靠,以及他如何能够提高它的可靠性。

    First, consider the question Oscar asked on his survey. Is his question a good survey question? Is the question unbiased? Good survey questions are short and concise and usually begin with “Who, What, When, Where, Why, or How.”
    ::首先,考虑奥斯卡在调查中提出的问题。 他的问题是否是调查的好问题? 问题是否公正? 问题是否公正? 良好的调查问题简明扼要,通常从“谁、什么、何时、何时、何地、为何或如何”开始。

    Next, consider Oscar's population and sample. What is Oscar's population? What is his sample? Are the participants in his sample randomly selected? Is his sample unbiased?
    ::接下来,考虑一下奥斯卡的人口和样本。奥斯卡的人口是什么?他的样本是什么?他的样本是什么?样本的参与者是随机挑选的吗?他的样本是否不带偏见?

    The answer is Oscar's survey is unreliable because: the survey question and sample are biased. Oscar should use a good survey question, such as "Do you eat the lunch served in the cafeteria? Why or why not?" or "What do you think of the lunch served in the cafeteria?" Oscar should ask his survey question to a random sample of students, not only the students who bring their own lunch. Oscar could ask every other 8th grader that leaves the cafeteria his survey question. This would ensure a randomly selected and large sample. 
    ::答案是Oscar的调查是不可靠的,因为:调查问题和抽样有偏差。Oscar应该使用一个良好的调查问题,比如“你吃自助餐厅提供的午餐吗?为什么不行?” 或“你对餐厅提供的午餐有什么看法?” Oscar应该向随机抽样的学生,而不仅仅是带午餐的学生,提出调查问题。Oscar可以向离开自助餐厅的其他8年级学生询问自己的调查问题。这将确保随机选择和大量抽样。

    Review
    ::回顾

    Use the information provided to answer the following questions.
    ::利用所提供的资料回答下列问题。

    One hundred people were asked to participate in a survey about travel. Participants were asked to state whether they had visited each of the cities listed below.
    ::要求100人参加旅行调查,要求与会者说明他们是否访问了下列每个城市。

    City Number of People Who Visited:
    Waikiki 85
    New York City 80
    San Francisco 87
    Chicago 54
    Dallas 35
    Orlando 38
    Atlanta 50
    Seattle 44
    Denver 32
    1. Create a bar graph of the data.
      ::创建数据中的条形图。
    2. What percent of the people visited Waikiki?
      ::有多少人去怀基基访问?
    3. What percent of the people visited Denver?
      ::有多少人去过丹佛?
    4. What percent of the people did not visit Dallas?
      ::有多少人没有去达拉斯?
    5. What percent of the people did not visit Chicago?
      ::有多少人没有去芝加哥?
    6. Which city had more people visited than any other city?
      ::哪个城市的访客比其他城市都多?
    7. Which city had less people visited than any other city?
      ::哪个城市的访客比其他城市少?

    Thirty students were selected at random at Montgomery High School. Each participant was asked to state the number of textbooks they were carrying at that moment. The results of the survey are depicted below. Choose the best display to depict the data. Then use the graph you created to answer the questions below.
    ::Montgomery高中随机挑选了30名学生,每个学员都被要求说明当时携带的教科书数量。下面将描述调查结果。选择最佳显示方式来描述数据。然后使用您创建的图表回答下面的问题。

    0 2 4 3 1 2 5 0 4 3 2 5 4 3 2 1 0 0 2 3 5 6 1 2 4 5 6 3 2 3

    1. Which graph is the best display of the data?
      ::哪个图表是数据的最佳显示?
    2. Create that graph here.
      ::在此创建此图 。
    3. What percent of the students had the most common amount of books in their backpack? (Round percent to the nearest hundredths place.)
      ::有多少学生的背包里有最普通的书籍? (百分百到最近的百分百位数的百分率。 )
    4. What percent of the students had between four and seven books in their backpack? (Round percent to the nearest hundredths place.)
      ::有多少学生背包里有4到7本书?
    5. How many students had 1 book in their backpacks?
      ::有多少学生背包里有一本书?
    6. How many students had 0 books in their backpacks?
      ::有多少学生背包里有0本书?
    7. What percent had 1 book? (Round percent to the nearest hundredths place.)
      ::有多少人有一本书?
    8. What percent had 0 books? (Round percent to the nearest hundredths place.)
      ::有多少人有零本书?

    Create a survey question. Decide who will be the sample population. Write a few sentences to describe who will take part in the survey and how you will administer the survey. Administer the survey, record the results on a table. Choose the most appropriate display for the data. Use these questions for guidance.
    ::创建一个调查问题。 决定谁将是抽样人口。 写几句话描述谁将参加调查以及如何管理调查。 管理调查, 将结果记录在表格中。 选择最适合的数据显示。 使用这些问题作为指导 。

    1. What is your sample population?
      ::你的抽样人口是多少?
    2. How many people are in the sample?
      ::样本中有多少人?
    3. Does your question use who, what, when, where or how?
      ::你的问题是否指谁、什么、何时、何地或如何?
    4. Is your sample biased, why or why not?
      ::你的样本有偏向吗? 为什么? 为什么?
    5. Are your results what you expected?
      ::你的结果和你预期的一样吗?

    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 。