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  • 解释Stem-and-Leaf 草图

    One of the benefits of stem-and-leaf plots is the clarity with which they display the actual numerical values of data points, while also presenting a clear visual indicator of the trends in the set. If you were given a stem plot depicting the money spent each week for a few months, how would you go about finding the parameters of the sample ?
    ::干叶地图的好处之一是清晰显示数据点的实际数字值,同时清晰地展示数据集趋势的直观指标。 如果给您一个描述每周花费数月的钱的干图,您将如何找到样本参数?

    Interpreting Stem-and-Leaf Plots
    ::解释Stem-and-Leaf 草图

    Stem plots can be a very efficient means of displaying the data in a set or sample. In fact, stem plots can be thought of as histograms ‘drawn’ by the data values themselves, rather than by bars representing those values, with bins separated by place value rather than otherwise designated intervals. From that point of view, stem plots are a type of histogram that may show more detailed information than standard histograms do, when the separation of bins by place value is appropriate (and it often is not). That means that many of the skills and terminology you have used with histograms applies also to stem plots.
    ::Stem 地块可能是在一组或样本中显示数据的一种非常有效的方法。 事实上,干块可以被数据值本身视为直方图的“拖动 ” , 而不是代表这些值的条形图,而以地值而不是其他指定间隔来分隔垃圾箱。 从这个角度看,干块是一种直方图,它可能比标准直方图显示更详细的信息,如果按地值分离垃圾箱是合适的(而且往往不是 ) 。 这意味着,在直方图中使用的许多技能和术语也适用于干块。

    As with histograms, range is an important characteristic in a stem plot. The range is the difference between the least and greatest values in the set. It can be important to note when a set appears to have a very large range, especially when there are very limited values in each stem, because it may indicate questionable data.
    ::与直方图一样, 射程是干茎图中的一个重要特征。 范围是集中最小值和最大值之间的差别。 当集似乎范围非常大时, 特别是当每根干茎的值非常有限时, 可能显示有问题的数据 。

    The shape of a stem plot carries the same general characteristics as a similar shape would if using a histogram:
    ::如果使用直方图,干块的形状具有与类似形状相同的一般特征:

    Bell-shaped: An obvious single and central area of the stem plot that has notably more members than the extremes do is referred to as a bell-shaped plot. This shape indicates that most of the values cluster around the , and quickly become less dense as we move away from the median and toward either of the extremes.
    ::Bell- 形状 : 干燥地块的一个明显的单一和中心区域, 其成员明显多于极端, 被称为钟形图。 这个形状显示, 大部分值围绕 . , 当我们从中位移向其中任一极端时, 其密度会迅速降低 。

    Uniform : A consistent width of each leaf suggests data that is not dramatically changed by the input. A very uniform stem plot is not particularly useful for identifying trends in the data, and may suggest a need to increase the number of place values in the stem in order to show more detail in each leaf. For example, a stem plot that appears nearly uniform with a stem only representing the hundreds place may show significantly more detail if the stem were set to represent the hundreds and tens places both, since this would create many more leaves.
    ::统一 : 每片叶的一致宽度表明数据不会因输入而发生巨大变化。 非常统一的干块对于确定数据趋势并不特别有用,而且可能意味着需要增加干叶中的位置值,以便显示每片叶的更多细节。 例如,一个看起来几乎一致的干叶块,仅代表数百个地方的干块,如果将干叶设成代表数百个和数十个地方,则可能显示得更详细得多,因为这将产生更多叶子。

    Skewed : As with the horizontal skewing of a histogram, stem plots with a obvious skew toward one end or the other tend to indicate an increased number of outliers either lesser than the mode (skewed down – correlating to a left-skew in a histogram) or greater than the mode (skewed up – correlating to a right-skewed histogram). Plots with an upward skew will have a mode that is smaller than either the mean or the median, and a mean that is greater than either the median or the mode. Downward-skewed plots will have a mean lesser than median or mode and a mode greater than either mean or median.
    ::斜形 : 与直方图的横向斜面一样, 向一端或另一端明显斜面的干块往往显示越来越多的外部线(斜向下(与直方图中的左键相关 ) ) , 或大于模式(斜向上(偏向上偏斜 — — 与右偏向直方图相关 ) 。 向上斜面的平面将有一个小于平均值或中位或中位的模式,以及一个大于中位或中位的平均值。 向下斜面的地块的平均值将低于中位或中位或中位,且比中位或中位或中位都大。

    Gathering Data from Stem Plots
    ::从 Stem 绘图收集数据

    Using the stem plot below, make a list of the number of hours that Isolde worked each week:
    ::使用下面的干草图, 列出Isolde每周工作时数列表:

    2 4 4 9 3 2 2 4 7 8 4 0 1 1 2 2 3 4 5 0 1 6 8

    Use the values in the left column to represent the tens place, and the values in the right column to represent the ones, and write each number out as a list:
    ::使用左栏中的值表示 10 位,右栏中的值表示 10 位,右栏中的值表示 10 位,并将每个编号写成列表 :

    Isolde’s work record (hours per week):
    ::伊索德的工作记录(每周小时):

    24, 24, 29, 32, 32, 34, 37, 38, 40, 41, 41, 42, 42, 43, 44, 50, 51, 56, 58

    Describing Stem Plots 
    ::描述 Stem 绘图

    Describe the type and meaning of the shape of the stem plot, identify the extremes, and state the mode(s) of the data. What does the data describe, as stated by the stem plot?
    ::描述干块形状的类型和含义, 标明极端, 并描述数据模式 。 数据描述什么, 如干块所示 ?

    Hathor's Expenses for Jan 2011
    1 2 4 5 5 8
    2 3 3 6 7 7 9
    3 0 0 3 3 3 7 8 8
    4 1 4 4 7
    5 0 2 3 3

    The data is bell-shaped, indicating that the majority of the data is clustered around the median. The median is 33, since there are 13 values above and below that point, and the extremes are 12 and 53 since those are the greatest and least values in the sample. The mode is 33, since there are 3 points with that value and no other value has more than 2 entries.
    ::数据为钟形,表示大部分数据集中在中位数周围。中位数为33,因为该点以上和下方有13个值,极端值为12和53,因为这些值是抽样中最大和最低的值。模式为33,因为有3个值,没有其它值超过2个条目。

    The plot describes the money spent in the month of January 2011, by someone named Hathor. Hathor bought mainly items less than $40, though there were a few purchases above the $40 mark, none were greater than $53.
    ::哈托尔(Hathor)主要购买了40美元以下的物品,尽管有几批采购超过40美元,但没有几批超过53美元。

    Comparing Data 
    ::比较数据

    Compare the weekly incomes of Sabah and Anaelle according to the stem plot below.
    ::根据以下干地比较萨巴赫和阿纳埃勒的每周收入。

    Week Income Comparison (USD)
    Sabah   Anaelle
    99 97 88 0 89 95
    79 23 1  
    93 68 42 2 09 17 22 58 77
    97 58 12 00 3 01 29 33 51 67 82

    Key: 147 = 1  |  47
    ::关键字:147=1=1=47

    a. What things stand out based on the shapes of the two plots, if any?
    ::a. 根据两块地的形状(如果有的话),哪些事情是突出的?

    Both plots are slightly up-skewed, indicating that the lower values are likely less indicative of the most common incomes. Sabah’s plot is otherwise pretty uniform, whereas Anaelle’s has a notably greater frequency of values in the $200 to $400 range.
    ::两块地块都略微偏斜,这表明低值可能不太能说明最常见的收入。 萨巴赫的地块本来是相当统一的,而阿纳埃勒的地块在200美元到400美元之间,其价值的频率明显更高。

    b. What is the place value of the stem?
    ::b. 干茎的地点价值是什么?

    The stem represents the hundreds place
    ::树干代表了数百个地方

    c. What does the blank on Anaelle's side next to the "1" indicate
    ::c. “1”字旁边Anaelle一侧的空白表示什么?

    Anaelle did not record any paychecks between $100 and $200.
    ::Anaelle没有记录任何100美元至200美元之间的工资支票。

    d. Who earned the most money overall?
    ::d. 总体而言,谁挣的钱最多?

    Without even totaling the columns, we can see that Anaelle earned more, as her column is heavily weighted towards the greater values, and she has also recorded an additional check.
    ::我们可以看到,Anaelle的收入更多,因为她的专栏大量加权到较大的值,她还记录了另外一张支票。

    e. Who had the most consistent paychecks?
    ::e. 谁有最一致的薪酬支票?

    Anaelle, as indicated by the greater number of checks clustered in the $200 - $400 range and few outliers.
    ::Anaelle指出,检查数量较多,集中在200至400美元的范围内,很少有外部出口。

    f. Who had the single greatest and who had the single least paycheck?
    ::f. 谁的薪酬最高,谁的薪酬最低?

    Sabah had the smallest paycheck at $88, and also the greatest at $397.
    ::萨巴赫的薪水最低,为88美元,也是最高,为397美元。

    g. Did they both record the same number of paychecks? 
    ::g. 两人的薪酬支票数是否相同?

    No, Anaelle recorded 13, Sabah only 12.
    ::不,安娜埃尔记录了13,萨巴赫只有12。

    Earlier  Problem Revisited
    ::重审先前的问题

    If you were given a stem plot depicting the money spent each week for a few months, how would you go about finding the various important parameters of the sample?
    ::如果给您一个描述每周花费数月的钱的干图, 你会如何找到样本中的重要参数?

    First look over the general shape of the plot to get an idea of the trend(s) of the data. Then identify the maximum and minimum extremes and the median and mode. Ask yourself if there are any particularly extreme outliers, or if the data is spread evenly, if there is there an obvious mode, if the median and the mode are close together, and if there are any other standout values. You can quickly get a good picture of the data by understanding how a stem plot works and applying your knowledge, but the data is useless if you don’t know how to read the data or what questions to ask.
    ::首先查看绘图的总体形状以了解数据的趋势。 然后确定最大和最小极端以及中值和模式。 问问你自己, 是否有特别极端的外向值, 或者数据是否平均分布, 是否有明显的模式, 中位值和模式是否接近, 是否有其他的显眼值。 您可以通过理解干图如何运作和应用知识, 快速获得数据的良好图象, 但是如果您不知道如何阅读数据或者需要问什么问题, 数据是毫无用处的 。

    Examples 
    ::实例

    The stem and leaf plot below shows the grade point averages of 18 students.
    ::下面的干叶块显示了18名学生的平均年级点。

    0 8 1 2 4 4 6 7 2 0 4 5 5 6 7 9 3 2 3 5 8 4 0

    Example 1
    ::例1

    What is the range of the data in the stem and leaf plot?
    ::干叶和叶片中的数据范围是多少?

    Range = maximum value − minimum value = 4.0 − 0.8 = 3.2
    ::范围=最大值-最低值=4.0-0.8=3.2

    Example 2
    ::例2

    How many students have a grade of 2 or more?
    ::有多少学生的年级为2级或2级以上?

    7 + 4 + 1 = 12  students
    ::7+4+1=12名学生

    Example 3
    ::例3

    What is the mode of the grades?
    ::成绩模式是什么?

    Two modes: 1.4 and 2.5
    ::两种模式:1.4和2.5

    Example 4
    ::例4

    What is the median of the grades?
    ::年级的中位数是多少?

    There are 18 data values and they are already ordered in the stem and leaf diagram.
    ::有18个数据值,在干叶图和叶图中已经订购了这些数据值。

    Median = ( t h e   9 t h   v a l u e   +   t h e   10 t h   v a l u e ) 2 = ( 2.5 + 2.5 ) 2 2.5 .
    ::中位值=( 第9次值+ 第10次值) 2 = (2.5+2.5) 22.5。

    Review 
    ::回顾

    True or False
    ::真实的或假的

    1. Some sets of data do not have a mean.
    ::1. 有些数据集没有含蓄的一套数据。

    2. There is always a mode for each set of data
    ::2. 每套数据总是有一个模式的

    3. The median is always a number in the data set.
    ::3. 中位数始终是数据集中的一个数字。

    Based on the following stem-and-leaf plot of student heights in inches, how tall is tallest person in class?
    ::根据以下学生身高(英寸)的干叶图, 班里最高的人有多高?

    4.

       
    4 5 7 8
    5 0 2 6 8 9
    6 0 2 4 7 8

    Taylor and some friends went crawdad hunting. The number of crawdads captured have been recorded below.
    ::Taylor和一些朋友去捕食龙虾,以下记录了抓获的龙虾数量。

    0 2 7 9
    1 0 4 7
    2 1 4 8
    3 3 6

    5. How many people went with Taylor?
    ::5. 有多少人和泰勒一起去?

    6. What were the total number of crawdads captured?
    ::6. 抓获的龙虾总数是多少?

    The following stem- and-leaf plot shows a range of 10 numbers.
    ::以下的干叶图显示有10个数字。

    87 5
    88 1 4 5
    89 1 7 7
    90 6 9

    7. What is the highest number?
    ::7. 最高数字是多少?

    8. What is the median value of the data set?
    ::8. 数据集的中值是多少?

    The back to back stem and leaf plot below shows the exam grades (out of 100) of two different class periods. The digit in the stem represents the tens and the digit in the leaf represents the ones.
    ::下面的背对背干和叶片图显示了两个不同班级的考试成绩(100分)。干叶中的位数代表了十位数,叶子中的位数代表了那些。

    Class Period 1   Class Period 2
    5 0 4 1 3 4 5
    3 3 2 1 5 3 4 5 5 7 9
    8 6 5 4 3 1 6 1 2 3 5 6 6 7 9
    9 7 6 3 1 0 0 7 0 3 4 6 8 9
    7 4 3 2 1 8 1 6
    5 3 2 0 9 0 1

    9. How many students scored higher than 60 in section 1?
    ::9. 有多少学生在第1节中得分超过60分?

    10. How many students scored higher than 60 in section 2?
    ::10. 有多少学生在第2节中得分超过60分?

    11. What are the minimum and maximum scores in section 1?
    ::11. 第1节中的最低分数和最高分数是多少?

    12. What are the minimum and maximum scores in section 2?
    ::12. 第2节中的最低分数和最高分数是多少?

    13. Without counting, which section has more students scoring 80 or more?
    ::13. 不计数,哪个科的学生得分超过80分或80分以上?

    14. Without counting, which section has more students scoring 50 or less?
    ::14. 不计数,哪个科的学生得分超过50分或不到50分?

    15. Describe the shape of the data set. Is it symmetric? Are there extreme values in the low or high numbers?
    ::15. 描述数据集的形状:是否对称?数字低或高是否有极端值?

    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 。