章节大纲

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    For his science class, Alex must present on the levels of air pollution in his city. He has collected readings, on 30 separate occasions, of the amount of carbon monoxide (CO) in the air in parts per million (PPM) below. He has organized his data in a table, but how can he create a data display that will clearly illustrate the air pollution? 
    ::亚历克斯在科学课上必须介绍他所在城市的空气污染程度。他在30个不同场合收集了以下百万分之一(PPM)部分空气中一氧化碳(CO)含量的读数。 他将数据整理成一张表格,但是他如何制作一个数据展示,以清楚地说明空气污染?

    In this concept, you will learn how to create and read frequency tables. 
    ::在此概念中,您将学会如何创建和阅读频率表。

    Creating and Reading Frequency Tables
    ::创建和阅读频率表格

    Data is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept you will analyze numerical data using frequency tables.
    ::数据是一组数字或非数字信息。数据可以多种不同方式分析。在此概念下,您将使用频率表分析数字数据。

    A frequency table  shows the frequency, or amount of occurrences, of a specific category or group of data. Said another way, a frequency table shows the number of times that a group of data occurred.
    ::频率表显示特定类别或数据组的频率或发生次数。换句话说,频率表显示一组数据发生的次数。

    Groups of data are referred to as bins . Bins can be many different sizes, but they never overlap. The size of the bins is determined by the range of the data.
    ::数据组称为文件夹。 文件夹可以是许多不同的大小, 但它们从不重叠。 文件夹的大小由数据范围决定 。

    The range  of a set of data is the difference between the largest and smallest values. The range identifies how far apart the values in the data set are. 
    ::一组数据的范围是最大值和最小值之间的差别。该范围确定数据集中值的距离。

    A frequency table has two columns, one for the bins (or categories) and the other for the number of occurrences. 
    ::频率表有两列,一列用于文件夹(或类别),另一列用于发生次数。

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

    Twenty people were asked how many hours they sleep each night. The results of the survey are listed below. Create a frequency table to display the data.
    ::20人被问及他们每晚睡几小时,调查结果如下:

    7, 8, 6, 9, 10, 12, 5, 7, 8, 9, 10, 11, 12, 7, 6, 7, 8, 10, 11, 9

    First, create a two column table. The left hand column will be the number of hours and the right will be the frequency. Since the range of the data is relatively small, each bin will be one hour. 
    ::首先,创建两个列表。左手列是小时数,右手列是频率。由于数据范围相对较小,每个文件箱为一小时。

    Sleep Data
    Bins: Number of Hours Slept Frequency
    5  
    6  
    7  
    8  
    9  
    10  
    11  
    12  

    Next, calculate the frequency of each bin. To do this, count up how many data points are 5 and place this value in the right column of the table. Then count up how many data points are 6 and place this value in the table. Continue until the entire table is complete. 
    ::下一步计算每个文件夹的频率。 要做到这一点, 请计数 5 个数据点, 然后将此值放在表格的右列中。 然后计数 6 个数据点, 然后将此值放在表格中。 继续直到整个表格完成 。

    The answer is the table should look like the one below.
    ::答案是,表格应该像下面的表格。

    Sleep Data
    Bins: Number of Hours Slept Frequency
    5 1
    6 2
    7 4
    8 3
    9 3
    10 3
    11 2
    12 2

    Let's look at another example.
    ::让我们再举一个例子。

    The data set below represents the amount of time (in minutes) 20 middle school students spent on the computer each day. Create a frequency table to display the data.
    ::下面的数据集代表每天20名中学生花在计算机上的时间(以分钟计),创建一个显示数据的频率表。

    10, 32, 8, 55, 5, 0, 30, 20, 25, 45, 40, 60, 45, 15, 5, 56, 47, 12, 15, 20

    First, create a two column table. The left hand column will be the number of hours and the right will be the frequency.
    ::首先,创建两个列表。左手列将是小时数,右手列是频率。

    Next, determine the size of the bins. The range of this data is from 0 to 60 minutes. Given this relatively larger range of data, we will create bins of size 10.
    ::下一步, 确定文件夹的大小。 此数据的范围为 0 至 60 分钟。 如果数据范围相对较大, 我们将创建大小为 10 的文件夹 。

    Computer Time
    Bins: Minutes Spent on Computer Frequency
    0-10  
    11-20  
    21-30  
    31-40  
    41-50  
    51-60  

    Next, calculate the frequency of each bin. To do this, count up how many data points are between 0 and 10, and place this value in the right column of the table. Then count up how many data points are between 11 and 20, and place this value in the table. Continue until the entire table is complete. 
    ::下一步计算每个文件夹的频率。 要做到这一点, 请计数 0 和 10 之间的数据点, 并将此值放在表格的右列中。 然后计数 11 和 20 之间的数据点, 并将此值放在表格中。 继续直到整个表格完成 。

    The table should look like the one below.
    ::表格应与下表相仿。

    Computer Time
    Bins: Minutes Spent on Computer Frequency
    0-10 5
    11-20 5
    21-30 2
    31-40 2
    41-50 3
    51-60 3

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Alex and his data on air pollution.
    ::早些时候,你被问及亚历克斯 和他关于空气污染的数据。

    Alex will present data on the amount of air pollution in his city. He organized his data into the table below. Alex's table is hard to read and does not clearly indicate the amounts of pollution. How can Alex create a table that will better represent the amount of pollution? 
    ::亚历克斯将提供有关其城市空气污染程度的数据。他将他的数据整理成下面的表格。亚历克斯的表格很难读,而且没有明确说明污染程度。亚历克斯如何能建立一个能够更好地代表污染程度的表格?

    City Air Pollution Data
    Date CO Level (PPM)
    2 May 4
    17 April 12
    12 May 15
    3 May 20
    6 May 20
    8 May 22
    18 April 25
    23 April 25

    9 May
    ::5月9日

    		27
    20 April 30
    25 April 30
    26 April 30
    27 April 34
    4 May 34
    28 April 36
    15 May 37
    30 April 38
    1 May 40
    16 April 42
    22 April 43
    5 May 45
    21 April 52
    7 May 55
    24 April 58
    10 May 58
    11 May 60
    19 April 63
    13 May 63
    14 May 71
    29 April 74

    Alex's data is not well organized and does not clearly indicate the amount of pollution that is present in the city. A frequency table would be a better way to display his data. 
    ::亚历克斯的数据没有很好地组织,也没有明确说明城市中的污染程度。 频率表是展示他数据的更好方法。

    To create a frequency table, first create a two column table. The left hand column of the table will be the amount of carbon monoxide (CO levels) in parts per million (PPM) and the right column will be the frequency. 
    ::要创建频率表, 请先创建两列表格。 表格的左手列将是百万分数的一氧化碳( CO 水平) , 右栏是频率 。

    Next, determine the size of the bins. The range of this data is from 4 to 74 PPM. Given this large range of data, we will create bins of size 10, starting at 0.
    ::下一步, 确定文件夹的大小。 此数据的范围为 4 到 74 PPM 。 鉴于此大范围的数据, 我们将创建大小为 10 的文件夹, 从 0 开始 。

    City Air Pollution 
    Bins: CO Level (PPM) Frequency
    0-10  
    11-20  
    21-30  
    31-40  
    41-50  
    51-60  
    61-70  
    71-80  

    Next, calculate the frequency of each bin. To do this, count up how many data points are between 0-10, and place this value in the right column of the table. Then count up how many data points are between 11-20, and place this value in the table. Continue until the entire table is complete. 
    ::下一步计算每个文件夹的频率。 为此, 请计算 0- 10 之间的数据点, 并将此值放在表格的右列中。 然后计算在 11-20 之间的数据点, 并将此值放在表格中。 继续直到整个表格完成 。

    The answer is the table should look like the one below. The frequency table below is a better visual representation of the data table that Alex started with. In reading the table, one can more easily see the frequency of the amount of pollution in Alex's city. 
    ::答案是表格应该像下面的表。下面的频率表是Alex开始的数据表的更直观的表示。在阅读表格时,人们可以更容易地看到亚历克斯城市污染程度的频率。

    City Air Pollution 
    Bins: CO Level (PPM) Frequency
    0-10 1
    11-20 4
    21-30 7
    31-40 6
    41-50 3
    51-60 5
    61-70 2
    71-80 2

      Example 2
    ::例2

    The data below shows the height (in meters) a ball bounced after being dropped from different heights. Create a frequency table to display the data. Then state one conclusion about the data. 
    ::下面的数据显示一个球从不同高度下降后弹出的高度(米)。创建一个显示数据的频率表。然后对数据给出一个结论。

    6 9 4 12 11 5 7 9 13 5 6 10 14 7 8

    First, create a two column table. The left hand column will be the height (in meters) and the right will be the frequency.
    ::首先,创建两个列表。左手列将是高度(米),右手列是频率。

    Next, determine the size of the bins. The range of this data is from 4 to 14 minutes. Given this relatively medium sized range of data, we will create bins of size 2, starting at 4.
    ::下一步, 确定文件夹的大小。 此数据的范围为 4 至 14 分钟。 鉴于此相对中等的数据范围, 我们将从 4 开始创建大小为 2 的文件夹 。

    Bounce Height
    Bins: Height (meters) Frequency
    4-5  
    6-7  
    8-9  
    10-11  
    12-13  
    14-15  

    Next, calculate the frequency of each bin. To do this, count up how many data points are between 4-5, and place this value in the right column of the table. Then count up how many data points are between 6-7, and place this value in the table. Continue until the entire table is complete. 
    ::下一步计算每个文件夹的频率。 要做到这一点, 请计算在 4-5 之间有多少数据点, 并将此值放在表格右列中。 然后计算在 6-7 之间有多少数据点, 然后将此值放在表格中。 继续直到整个表格完成 。

    Next, analyze the data by looking at the frequencies of the heights and state one conclusion. 
    ::接下来,通过观察高度的频率来分析数据 并给出一个结论

    The first answer is the table should look like the one below. The second answer is one conclusion that can be stated about the data is: when dropped the ball most frequently reached a height of 6 or 7 meters. 
    ::第一个答案是,表应该像下面的表。第二个答案是,关于数据的一个结论是:当投下球时,最常达到6米或7米的高度。

    Bounce Height
    Bins: Height (meters) Frequency
    4-5 3
    6-7 4
    8-9 3
    10-11 2
    12-13 2
    14-15 1

    Example 3
    ::例3

    Kelsey asked her classmates how long they went on vacation for over the summer. Below is the data Kelsey collected. 
    ::Kelsey问她的同学暑假多久了,下面是Kelsey收集的数据。

    • 1 classmate was gone for 8 days
      ::一个同学走了8天
    • 18 classmates were gone for 9 days
      ::18个同学走了9天
    • 16 classmates were gone for 10 days
      ::16个同学走了10天
    • 6 classmates were gone for 11 days
      ::6个同学离开11天
    • 9 classmates were gone for 12 days
      ::9个同学走了12天
    • 4 classmates were gone for 13 days
      ::4个同学离开13天

    Create a frequency table the represents Kelsey's data. Then state two conclusions about the data. 
    ::创建显示 Kelsey 数据的频率表。 然后对数据给出两个结论 。

    First, create a two column table. The left hand column will be the vacation days and the right will be the frequency.
    ::首先,创建两个列表。左手列将是休假日,右手列是频率。

    Next, determine the size of the bins. The range of this data is relatively small. Given this, we will create bins of size 1, starting at 8.
    ::下一步, 确定文件夹的大小。 此数据的范围相对较小 。 有鉴于此, 我们将创建大小为 1 的文件夹, 从 8 开始 。

    Next, calculate the frequency of each bin. In this case, Kelsey has already done this as represented in her list. Use her values to fill in the entire table. 
    ::接下来,计算每个垃圾箱的频率。 在这种情况下, Kelsey 已经按其列表中的表达方式做了此操作。 使用她的数值填入整个表格 。

    Next, analyze the data by looking at the frequencies of the vacation days and state two conclusions. 
    ::接下来,通过查看休假日的频率分析数据,并提出两个结论。

    The first answer is the table should look like the one below. The second answer is two conclusions are: the most frequent vacation length among classmates was 9 days; and the least frequent vacation length among classmates was 1 day.
    ::第一个答案是表应该像下面的表。第二个答案是两个结论:同学最常见的假期是9天;同学中最不经常的假期是1天。

    Vacation Days
    Bins: Vacation Days Frequency
    8 1
    9 18
    10 16
    11 6
    12 9
    13 4

    Example 4
    ::例4

    The frequency table below lists the scores of a class on two separate exams. Compare and contrast the test scores and explain which test was more challenging. 
    ::下面的频率表列出了两个不同的考试中一个班级的分数。比较和对比测试分数,并解释哪个考试更具挑战性。

    Class Scores
    Bins: Test Score (%) Frequency Test 1 Frequency Test 2
    0-50 0 5
    51-60 2 3
    61-70 7 4
    71-80 10 7
    81-90 5 8
    91-100 6 3

    First, analyze the data by comparing the frequencies of scores between test 1 and test 2. Then, determine which test was more challenging. 
    ::首先,通过比较试验1和试验2之间的分数频率来分析数据,然后确定哪项试验更具有挑战性。

    The answer is test 2 was more challenging, because (a) there was a greater distribution of scores across all bins than test 1 and (b) there were a greater number of students who scored 70 or less.
    ::答案是测试2更具有挑战性,因为(a) 在所有垃圾箱的得分分配比测试1要多;(b) 得分70分或70分以下的学生人数更多。

    Review
    ::回顾

    Use each set of data to answer the following questions.
    ::使用每套数据回答下列问题。

    There are 175 7th grade students. Here is a list of the number of days that 7th students at Marrimack Middle School bought lunch.
    ::有175名七年级学生,这是Marrimack中学七年级学生购买午餐的天数清单。

    0 Days = 15 students
    ::0天=15名学生

    1 Day = 13 students
    ::1天=13名学生

    2 Days = 30 students
    ::2天=30名学生

    3 Days = 21 students
    ::3天=21名学生

    4 Days = 35 students
    ::4天=35名学生

    5 Days = 60 students
    ::5天=60名学生

    1. How many students are in the 7 t h grade?
      ::七年级有多少学生?
    2. What is the most popular number of days?
      ::最受欢迎的天数是多少?
    3. What is the least popular number of days?
      ::最不受欢迎的天数是多少?
    4. Create a frequency table to show the data.
      ::创建显示数据的频率表。
    5. Were any students left out of the count?
      ::有任何学生被忽略在计数之外吗?
    6. How do you know?
      ::或笵
    7. Create a frequency table to display the data below.
      ::创建频率表以显示以下数据 。

    2, 5, 3, 1, 6, 5, 7, 8, 3, 1

    1. Were there any numbers not represented?
      ::是否有人数没有代表?
    2. What is the most popular number or numbers?
      ::什么是最受欢迎的数字或数字?

    The following frequency table shows data regarding the number of people who attended different movies in one week. Use the following frequency table to answer each question.
    ::以下的频率表显示了一周内参加不同电影的人数的数据。使用以下的频率表回答每个问题。

    # of People at the movies per week Frequency
    20 4
    50 3
    85 3
    90 5
    120 2
    1. If we were to create a list of this data, is the following list correct or incorrect:
      ::如果我们要创建这一数据的清单,以下清单是否正确或不正确:

    20, 20, 20, 20, 50, 50, 50, 90, 90, 90, 85, 85, 85, 120, 120

    1. How many showings had 90 people or more in attendance?
      ::有多少节目有90人或超过90人出席?
    2. How many showings had less than 50 people in attendance?
      ::有多少节目有不到50人出席?
    3. How many showings had less than 70 people in attendance?
      ::有多少节目有不到70人出席?
    4. True or false. This data also tells you which showings had the most people in attendance.
      ::真实的或虚假的。这些数据还显示哪些显示显示的出席人数最多。
    5. True or false. There were two showings that had 78 people in attendance.
      ::有两部电影有78人出席

    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 。

    Resources
    ::资源