Section outline

  • General

    Collapse all Expand all

  • 创建 Stem- and- Leaf 图表

    If you were asked to make a stem and leaf plot of the number of hours that Brian worked each month, given the data below, would you know or remember how? By the end of this lesson you will!
    ::如果有人要求你绘制布赖恩每月工作时数的干叶图,根据以下数据,你会知道或记得如何做吗?在课程结束时,你会!

    Make a stem plot of the number of hours that Brian worked each month:
    ::布赖恩每月工作时数的干细图如下:

    Hours per month: 137, 149, 142, 121, 135, 133, 138, 137, 129, 139, 126, 139
    ::每月时数:137、149、142、121、135、133、138、137、129、139、126、139

    Stem-and-Leaf Plots 
    ::Stem-and-Leaf 草地

    Stem-and-Leaf plots, also known as stem plots, are similar to sideways histograms, but are more descriptive because they are built by displaying the specific values of individual data points. Histograms are more visual and can be more striking and/or creative, but stem plots can be more accurate and can make further study of the data more efficient.
    ::Stem-and-Leaf 地块,又称干地,与侧形直方图相似,但更具描述性,因为它们是用显示单个数据点的具体值来构造的。 直方图更具有视觉性,更能吸引人和(或)更具有创造性,但干地可以更准确,更能提高数据进一步研究的效率。

    Creating a stem plot is not difficult, but, like most things, is easier and quicker with practice. To begin creating your stem plot, start by making two columns and labeling one leaf and the other stem . You can either create a full table, like this one:
    ::创建干块并不难, 但和大多数事情一样, 实践会更容易和更快。 要创建干块, 首先绘制两条柱子, 并标注一叶和另一根干。 您可以创建一个完整的表格, 比如这个表格 :

    Stem Leaf
    0 0
    0 0
    0 0

    Or you can make one out of simple characters, like this:
    ::或者你可以用简单的字符来做一个,像这样:

    Stem Leaf 0 0 0 0 0 0

    ::斯泰姆Leaf000

    Just be sure that it is easy to see which column your values are placed in when the data is entered.
    ::只需确定在输入数据时很容易看到您的数值放在哪个列中。

    Depending on the size of your numbers, your stem column will either represent the single greatest place value of your data points, or perhaps the two or more greatest place values. The leaf column will represent the smallest place value(s) of the set. If you are listing multiple place values in either column, make a key such as the one below easily visible.
    ::取决于您数字的大小, 您的干柱将代表您数据点的最大位置值, 或者可能是两个或两个以上位置值。 叶子列将代表集的最小位置值。 如果您在任意一列中列出多个位置值, 请让一个键像下面的键那样容易可见 。

    Key: 53,243
    ::关键:53 243

    53 | 243

    If you have two different related sets of data to compare (or bivariate data), you can use a back-to-back version of the plot. The back-to-back version places the stem in the center of three columns, and the different leaves on each side, as below. Note that ordering the data on the plot requires that you arrange the values so that they increase from the center out, rather than just from left to right.
    ::如果您有两套不同的相关数据要比较(或双变量数据),您可以使用一个背对背版本的绘图。背对背版本将干柱放在三列的中间,并将不同的叶子放在每一边,如以下。请注意,在绘图上订购数据需要您安排数值,以便从中间向外增长,而不是从左向右增长。

    Leaf Stem Leaf
    3 2 1 0 0 0 1 2 3
    3 2 1 0 1 0 1 2 3
    3 2 1 0 2 0 1 2 3

    Whatever the purpose of your stem plot, always be certain to label the plot clearly!
    ::无论你干草图的目的是什么 一定要把图画标得清楚明了

    Constructing Stem-and-Leaf Plots 
    ::正在构造 Stem- and- Leaf 绘图

    1. Make a stem plot of the money that Jelani spent this month:
    ::1. 将杰拉尼本月花费的钱编成干细图:

    Jelani’s purchases: $59, $54, $49, $68, $62, $74, $57, $30, $40, $80, $86
    ::Jelani的采购:59、54、49、68、62、74、57、30、40、80、86

    Start by creating your table with the heading, stem and leaf columns labeled:
    ::从创建表格开始,以标题、干叶和叶柱标注:

    Jelani's Purchases for the Month
    Stem (tens) Leaf (ones)
       

    Then begin to insert the data, creating a single row for each tens place:
    ::然后开始插入数据,为每 几十 个位创建单行 :

    Jelani's Purchases for the Month
    Stem (tens) Leaf (ones)
    3  
    4  
    5  
    6  
    7  
    8  

    Finally, fill in the leaves with the ones place values indicated by your data, listing them in increasing numerical order:
    ::最后,在树叶中填写您数据所示的位置值,并按增加的数值顺序列出:

    Jelani's Purchases for the Month
    Stem (tens) Leaf (ones)
    3 0
    4 0 9
    5 4 7 9
    6 2 8
    7 4
    8 0 6

    2. Beryl loves basketball, and she tracked the number of points her favorite pro player scored in the first 25 games of his last season. Create a stem plot of the data.
    ::2. 贝里尔热爱篮球,她追踪了她最喜欢的职业球员在上个赛季前25场比赛中得分的分数,绘制了数据干图。

    Points per game: 25, 41, 47, 42, 20, 37, 38, 40, 33, 21, 27, 46, 42, 28, 23, 35, 29, 42, 31, 45, 25, 27, 33, 37, 42
    ::每场比赛:25、41、47、42、20、27、38、40、33、21、27、46、42、28、23、35、29、42、31、45、25、27、33、37、42

    Notice that the data points are all between 20 and 50, so we will need only 3 stems in our plot, each of which will have quite a few leaves. Because there are so many points, it might be worth the time to first organize the data in increasing numerical order:
    ::请注意,数据点在20到50之间, 所以我们只需要在我们的地块里有三根, 每个地块都有相当多的叶子。 因为有这么多点, 可能值得先用增加的数值顺序来组织数据:

    20, 21, 23, 25, 25, 27, 27, 28, 29, 31, 33, 33, 35, 37, 37, 38, 40, 41, 42, 42, 42, 42, 45, 45, 47

    Now it is a simple matter to place all of the correct leaves in the proper column:
    ::现在,将所有正确的叶子放在正确的柱子上是一个简单的问题:

    Points Scored per Game
    Stem (tens) Leaf (ones)
    2 0 1 3 5 5 7 7 8 9
    3 1 3 3 5 7 7 8
    4 0 1 2 2 2 5 5 7

    3. Create a stem plot to compare the hours that Bruna and Giselle each worked per week during the same three months of last year:
    ::3. 建立一个干线图,比较去年3个月中Bruna和Giselle每人每周工作的时间:

    Bruna hours worked: 40, 31, 40, 31, 36, 36, 20, 21, 40, 33, 31, 50, 47, 34
    ::工作时数:40、31、40、31、36、36、20、21、40、33、31、50、47、34

    Giselle hours worked: 28, 23, 35, 29, 42, 31, 45, 25, 27, 34, 31, 40, 32, 41
    ::Giselle工作时间:28、23、35、29、42、31、45、25、27、34、31、40、32、41

    First sort the data in ascending numerical order:
    ::以向上数字顺序排列的第一种数据类型 :

    Bruna hours worked: 20, 21, 31, 31, 31, 33, 34, 36, 36, 40, 40, 40, 47, 50
    ::工作时数:20、21、31、31、31、33、34、36、36、40、40、40、47、50

    Giselle hours worked: 23, 25, 27, 28, 29, 31, 31, 32, 34, 35, 40, 41, 42, 45
    ::Giselle工作时间:23、25、27、28、29、31、31、31、32、34、35、40、41、42、45

    Next create a labeled three column table with the tens column in the center and the ones column for each person on the sides, note that all of the values are between 20 and 50, so we will need only 4 rows. List the values in increasing numerical order from the center out!
    ::下一个创建标签的三列表格, 中间有十列, 边上有每个人的一列, 注意所有值都在20到50之间, 所以我们只需要四行。 列出从中间增加数字顺序的数值 !

    Hours Worked per Week
    Bruna   Giselle
    1 0 2 3 5 7 8 9
    6 6 4 3 1 1 1 3 1 1 2 4 5
    7 0 0 0 4 0 1 2 5
    0 5  

    Earlier  Problem Revisited
    ::重审先前的问题

    Make a stem plot of the number of hours that Brian worked each month:
    ::布赖恩每月工作时数的干细图如下:

    Hours per month: 137, 149, 142, 121, 135, 133, 138, 137, 129, 139, 126, 139
    ::每月时数:137、149、142、121、135、133、138、137、129、139、126、139

    First arrange the values in ascending numerical order:
    ::首先按向上数字顺序排列值:

    121, 126, 129, 133, 135, 137, 137, 138, 139, 139, 142, 149

    Now create your table, listing the first two place values in the stem column (since these are all three-digit numbers):
    ::现在创建您的表格, 在干柱中列出前两个位数值( 因为这些数字都是三位数 ) :

    Hours Brian Worked Each Month:
    ::Brian每月工作:

    12 1 6 9 13 3 5 7 7 8 9 9 14 2 9

    Key: 147 = 14  |  7
    ::关键字:147=14=7

    Examples
    ::实例

    Example 1
    ::例1

    If you asked to make a stem and leaf plot from the following test scores, what would be the first step? 73, 99, 92, 91, 85, 82, 76, 92, 80, 70, 9, 59, 91, 95, 86, 77, 78, 71, 64, 82, 98, 65, 56
    ::如果你要求从以下考试分数中绘制干叶图,第一步是什么?73、99、92、91、85、82、76、92、80、70、9、59、91、95、86、77、78、71、64、82、98、65、56

    The first step would be to put the scores in numerical order so that they looked like this: 56, 59, 64, 65, 69, 70, 71, 73, 76, 77, 78, 80, 82, 82, 85, 86, 91, 91, 92, 92, 95, 98, 99
    ::第一步是按数字顺序排列得分,使其看起来象:56、59、64、65、69、70、71、73、76、77、78、80、82、82、85、86、91、91、92、92、95、98、99

    Example 2
    ::例2

    What is the range of the data? Once the range has been identified, what is going to be the range of the stem and wny? 
    ::数据的范围是什么?一旦确定范围,干和干的范围是什么?

    The range of the data is from 56 to 99. Therefore the stems, identified by the 10’s place value, will range from 5 to 9
    ::数据范围在56至99之间,因此,根据10人的地点价值确定的根值,在5至9之间。

    Example 3
    ::例3

    Create a stem-and-leaf plot for this data. 
    ::为此数据创建干页图 。

    Your plot should look like this:
    ::您的情节应该是这样的:

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

    Example 4
    ::例4

    What kind of graph would this be if it was turned vertically?
    ::如果垂直转动会是什么图表呢?

    A Histogram
    ::直方图

    Example 5
    ::例5

    In which interval did the least number of students score? In which did the most students score? 
    ::学生得分最低的间隔是哪一段?学生得分最多的是哪一段?

    The first stem: 50 to 59, contains the least number of values, 2 of them. The 70 - 79, and 90 - 99 stems each had 6 scores, for the high.
    ::第一个点:50到59, 包含最少的值, 其中2个值。70到79, 90到99根, 每人6分, 最高。

    Review 
    ::回顾

    Make a stem-and-leaf plot from the following data. The data represents the number of times in the last year that each polled student attended a school function.
    ::从以下数据中绘制干叶图。 数据代表了去年每个受访学生参加学校活动的次数 。

    Number of functions attended: 17, 16, 16, 16, 16, 15, 15, 19, 18, 17, 15, 13, 14, 15, 23, 12, 36, 48, 45, 28, 23, 24, 18, 17, 16, 15, 16, 13, 17, 19, 14, 15, 17, 12
    ::参加的职务数目:17、16、16、16、16、16、15、15、15、19、18、17、15、13、13、14、15、23、12、36、48、45、28、23、24、18、17、16、15、16、16、13、17、19、14、15、17、12

    1. Based on the data, how many total students were polled?
    ::1. 根据数据,有多少学生接受民意测验?

    2. What interval represents the least number of functions attended by students?
    ::2. 学生参加工作次数最少的间隔是多少?

    3. What interval represents the greatest number of functions attended by students?
    ::3. 学生参加工作的时间间隔是多少?

    Create stem-and-leaf plots for the following sets of data.
    ::为以下数据集创建干页图。

    4. Fifteen people were asked how often they bought flavored coffee on their way to work during the last 10 working days. The number of times each person bought flavored coffee was as follows: 5, 7, 9, 9, 3, 5, 1, 0, 0, 4, 3, 7, 2, 9, 8
    ::4. 15人被问及,在过去10个工作日里,在上班途中,他们经常购买口味咖啡,每人购买口味咖啡的次数如下:5、7、9、9、3、5、1、0、0、4、3、7、2、9、8

    5. A middle school teacher asked her students how many books they had read over the last year. Their reported answers were as follows: 13, 22, 20, 5, 11, 6, 14, 26, 20, and 13.
    ::5. 一名中学教师问她的学生去年读过多少本书,他们报告的答复如下:13、22、20、25、11、6、14、26、20和13。

    6. Joe is training for a swim meet, and keeps track of the number of laps he swims each day. Create a stem-and-leaf plot to organize the data: 21, 22, 23, 18, 28, 27, 24, 24, 28, 29, 24, 20, 27, 28, 21, 40, 21, 9, 27, 23, 28, 27, 25, 27, 19, 31, 30, 24, 30, 28.
    ::6. Joe正在训练游泳会,并记录他每天游泳的圈子数目,制作一个干叶图来组织数据:21、22、23、18、28、27、24、24、28、29、24、20、27、28、21、40、21、9、27、23、28、27、25、27、27、19、31、30、34、30、34、30、38。

    7. Redraw the stem and leaf plot, using the above data using 5-unit intervals.
    ::7. 利用上述数据,使用5个单位的间隔来重新绘制干叶和叶片。

    8. Comment on how the data looks different, and explain which chart you feel is a better representation, and why.
    ::8. 评论数据看起来如何不同,并解释你认为哪个图表更能说明问题,并说明原因。

    The weights to the nearest kilogram of 30 kids were recorded. 59.1, 61.6, 62.2, 61.5, 60.8, 59.9, 60.4, 59.1, 61.0, 60.8, 61.5, 56.2, 61.8, 65.6, 60.3, 58.8, 59.0, 61.3, 62.0, 61.3, 58.5, 60.9, 60.3, 62.6, 60.1, 59.2, 61.8, 61.8, 58.5, 62.1
    ::30名儿童的体重与最接近的公斤数有记录。 59.1、61.6、62.2、61.5、60.8、59.9、60.4、59.1、61.0、60.8、61.8、61.5、56.2、61.8、65.6、60.3、58.8、59.8、61.0、61.3、62.0、61.3、58.5、60.9、60.3、62.6、60.6、60.1、59.2、61.8、61.8、58.5、62.1。

    9. What numbers will be represented by the stem? What numbers will be represented by the leaf?
    ::9. 干叶代表哪些数字?叶子代表哪些数字?

    10. What is the data range? Where will the stems start and finish?
    ::10. 数据范围是什么?根从何处开始和结束?

    11. Create a stem-and-leaf plot for the data.
    ::11. 为数据绘制一个干叶图。

    12. Which weights would be considered outliers?
    ::12. 哪些权重可被视为外部值?

    You are the football coach & you have two place-kickers. Manny has made field-goals of 23 yards, 34 yards, 30 yards, 23 yards, and 28 yards, but has missed field goals of 16, 16 and 23 yards. The other, Jose, has made field goals of 11 yards, 16 yards, 21 yards, 20 yards, but has missed field goals of 26 and 28 yards. There is only 15 seconds left on the play clock.
    ::你们是足球教练,你们有2个打球场,曼尼的球场目标为23码、34码、30码、23码、28码,但错过了16码、16码和23码。另一个是何塞的球场目标为11码、16码、21码、20码,但是却错过了26码和28码的球场目标。游戏时钟只剩下15秒。

    13. Create Stem-and-Leaf plots to represent the Manny’s data.
    ::13. 创建Stem-and-Leaf地块以代表曼尼的数据。

    14. Create Stem-and-Leaf plots to represent the Jose’s data.
    ::14. 创建Stem-and-Leaf地块以代表Jose的数据。

    15. Your team can win the state championship if your kicker makes an 18 yard field-goal. Which kicker would you choose & why?
    ::如果你的踢球手能达到18个场场目标,你的球队就能赢得州冠军。 你会选择哪个踢球手? 为什么?

    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 。