章节大纲

  • What Does the Fox Say?
    ::狐狸说什么?

    Red fox walking in a snowy environment, showcasing its natural habitat.
    Red Fox

    Many studies require multiple samples to be taken. Multiple samples are used when the conditions change. Conditions may include location, as in the following example, or any variable that could potentially influence the results.
    ::许多研究要求采集多个样本。当条件发生变化时,会使用多个样本。条件可能包括地点,如下例,或可能影响结果的任何变量。

    Example
    ::示例示例示例示例

    Jared is a zoologist who is measuring the length of red foxes. He plans to use several samples, with each sample comprised of the length of ten foxes in centimeters. He has taken three samples from three different locations so far, and his results are in the interactive below.
    ::贾里德是一位测量红狐长度的动物学家。他计划使用几个样本,每个样本由10只狐狸的厘米长度组成。 他迄今已从三个不同地点采集了三个样本,其结果在下文互动。

    Use the interactive to explore how one value can affect the outcome of a sample.
    ::使用互动来探索一个值如何影响样本的结果。

    Variability of Samples 
    ::样本的可变性

    In the example above,  you saw that different samples could have different results. These differing outcomes do not directly signal any mistakes in the testing process or error among the results. The difference between samples merely shows the variability during the testing process.  Variability of samples is linked to the idea of the measure of variability that was  explored in .
    ::在以上的例子中,您看到不同样本可能有不同的结果。这些不同的结果并不直接表示测试过程中的任何错误或结果中的任何错误。样本之间的差异只是显示了测试过程中的变异性。样本的可变性与在(......)中探讨的可变性计量概念有关。

    If  you measure the length of 10 foxes, all 10 foxes will likely not have the same length. As a result of the measure of variability, if  you study 10 samples of multiple foxes each, all 10 samples will likely not have the same mean. The variability of samples reflects the variability of the population . In this case, the more samples that are taken, the more closely your overall data will display the heights of red foxes making up the entire population.
    ::如果你测量了10只狐狸的长度,那么所有10只狐狸的长度都不可能是相同的。由于量度差异,如果每只研究10个多狐狸的样本,所有10只样本都可能不是相同的平均值。样本的变异性反映了人口的变异性。在这种情况下,所采集的样本越多,你的总体数据就越能显示构成整个人口的红色狐狸的高度。

    Use the interactive below to explore what happens when more samples are taken.
    ::使用下面的交互方式来探索在采集更多样本后会发生什么情况。

    INTERACTIVE
    Sample Variability in Fox Lengths
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    • Press the button to take a sample of the length of 10 foxes and record the mean. 
      ::按下按钮来抽样 10只狐狸的长度 并记录平均值。
    • Another button will appear which can help you take more samples of 10 foxes at a time.
      ::将出现另一个按钮,它可以帮助您每次采集更多10只狐狸的样本。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. As you take more samples, what do you notice?
      ::当你采集更多的样本时,你注意到什么?
    2. What do you think the mean length of a red fox is? How confident are you?
      ::你觉得红狐狸的长度是多少?
    3. How confident are you that the mean value of a red fox is between 35 and 51?
      ::你有多有信心 红狐的平均值在35到51之间?
    4. How can this information be useful to Jared?
      ::这一信息如何能对Jared有用?

    Going Electric
    ::电 电 电 电

    Sam wants to know how many people in her city car own an electric car. She decides to take 10 samples of 50 people. Before taking her samples, Sam decides that she will only ask people over the age of 18. Additionally, Sam decides to ask people in 10 different locations in the city. Buying a car is a purchase and Sam lives in a socioeconomically diverse city. Taking a sample from different locations will give her more representative data for the whole city. The results from Sam’s samples are below:
    ::Sam想知道她的城市汽车里有多少人拥有电动汽车。她决定采集50人的10个样本。在采集样本之前,Sam决定她只询问18岁以上的人。在采集样本之前,Sam决定她只询问18岁以上的人。此外,Sam决定询问城市内10个不同地点的人。购买一辆汽车是一种购买,Sam住在一个具有社会经济多样性的城市里。从不同地点采集的样本将给她提供全市更具代表性的数据。Sam的样本结果如下:

    • Sample 1 – 0/50
      ::样本1 - 0/50
    • Sample 2 – 1/50
      ::样本2 - 1/50
    • Sample 3 – 2/50
      ::样本 3 - 2/50
    • Sample 4 – 0/50
      ::样本 4 - 0/50
    • Sample 5 – 0/50
      ::样本 5 - 0/50
    • Sample 6 – 0/50
      ::样本 6 - 0/50
    • Sample 7 – 1/50
      ::样本 7 - 1/50
    • Sample 8 – 1/50
      ::样本 8 - 1/50
    • Sample 9 – 0/50
      ::样本 9 - 0/50
    • Sample 10 – 0/50
      ::样本 10 - 0/50

    Sam found the following results: 0, 0.02, 0.04, 0, 0.02, 0, 0.02, 0.06, 0.02, 0. The combined average of these ten values is 0.018. This can be written as a percentage:
    ::Sam发现了以下结果:0, 0.02, 0.04, 0, 0.02, 0, 0.02, 0, 0.02, 0.02, 0.0。 这十个数值的总平均值是0.018。 这可以以百分比表示:

    0.018 × 100 = 1.8 %

    Discussion Questions
    ::讨论问题 讨论问题

    1. How can this percentage be useful in estimating the number of people in the city that own an electric car?
      ::这百分比如何有助于估计城市内拥有电动汽车的人数?
    2. How could Sam get an exact number?
      ::萨姆怎么会有确切的号码?
    3. How could this information be useful?
      ::这种信息如何有用?

    Collecting Data
    ::收集数据

    Use the interactive below to collect and display the information collected from different people.
    ::使用下面的交互方式收集和显示从不同人群收集的信息。

    INTERACTIVE
    Collecting Data By Catching Bugs
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    You will be recording the time it takes for you to catch a bug on the screen 5 times. Then do so with 3 other classmates and observe the statistics for your results.
    ::您将记录您在屏幕上捕捉窃听器5次所需的时间。 然后与其他3名同学一起这样做, 并观察您结果的统计数据 。

    • Press the buttons to release the bug.
      ::按下按钮释放错误 。
    • Tap the bug to catch it and stop the timer.
      ::窃听窃听器来抓住它 并停止计时器。
    • Observe the the results for each student in the given table.
      ::观察表格中每个学生的成绩。
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    Using the above interactive, collect data from yourself and from 4 other classmates. Each classmate should provide 5 samples. Display each sample in a spreadsheet. Find the  mean and MAD for each person's data.
    ::使用上述互动方式, 向您和其他4位同学收集数据, 每个同学应提供5个样本, 在电子表格中显示每个样本, 找到每个人数据的平均值和 MAD 。

    Discussion Questions
    ::讨论问题 讨论问题

    1. How can we tell whether the results from the samples are different or if they reflect the variability of the data?
      ::我们如何判断样品的结果是否不同,或者它们是否反映了数据的可变性?
    2. Does the mean average deviation in the data lead you to believe that the variance that you see in the data is normal for the population?
      ::数据的平均平均偏差是否使你相信数据中看到的差异对人口来说是正常的?
       
    • A measure of center is a “typical” value that describes a data set . 
      ::中心度量是一个描述数据集的“典型”值。
    • A measure of variability is a number that is used to describe the spread of a data set.
      ::衡量可变性的尺度是用来描述数据集分布的数字。
    • The mean of a data set (also known as the average) is the sum of the data values divided by the number of data values in the set.
      ::数据集的平均值(也称为平均值)是数据值除以数据集中数据值数的总和。
    • The mean absolute deviation (MAD) is the measure of variability that is used to measure how spread out the values in the data set are.
      ::平均绝对偏差(MAD)是用于衡量数据集中数值分布方式的可变性度。