4.18散点图

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 散点图

  Collapse Expand

  散点图

  

  [Figure 1]

  播放段落

  William is interested in global warming and climate change. He's noticed that the summers seem to be pretty hot, but there have been some really bad snow storms in the winter as well so he's not sure what global warming is all about. He does some research and finds the following  scatter plot .
  ::威廉对全球变暖和气候变化感兴趣。他注意到夏天似乎很热, 但冬天也发生了一些非常糟糕的雪暴, 所以他不知道全球变暖到底是怎么回事。他做了一些研究,发现了以下的散落地块。

  

  [Figure 2]

  播放段落

  This scatter plot shows the  average  temperature for the whole Earth each year since 1880. How should William interpret this scatter plot? Does it show a  correlation  between year and annual average global temperature?
  ::这个散射图显示自1880年以来整个地球每年的平均温度。 威廉应该如何解释这个散射图? 它是否显示年与年平均全球温度的相关性?

  播放段落

  In this concept, you will learn how to make and read scatter plots of paired real-world  data  to recognize patterns and make predictions.
  ::在这个概念中,你将学会如何制作和阅读成对的现实世界数据,以识别模式和作出预测。

  播放段落

  Constructing and Reading Scatter Plots
  ::构造和读取散列绘图

  播放段落

  A  scatter plot  is a type of graph that shows pairs of data plotted as points.
  ::散射图是一个图表类型,显示作为点绘制的对数据。

  播放段落

  You can use a scatter plot to  analyze   trends  in your data and to help you to determine whether or not there is a relationship between two variables. A scatter plot can show a positive relationship, a negative relationship, or no relationship.
  ::您可以使用散射图分析数据中的趋势, 帮助您确定两个变量之间是否有关系。 散射图可以显示正关系、 负关系或无关系 。

  

  [Figure 3]

  播放段落

  If the points on the scatter plot seem to form a line that slants up from left to right, there is a  positive relationship  or  positive correlation  between the variables.
  ::如果散射图上的点似乎形成一条线,从左向右倾斜,则变量之间有正关系或正相关关系。

  播放段落

  If the points on the scatter plot seem to form a line that slants down from left to right, there is a  negative relationship  or  negative correlation  between the variables.
  ::如果散射图上的点似乎形成一条线,从左向右倾斜,则变量之间有负关系或负相关关系。

  播放段落

  If the points on the scatter plot seem to be scattered randomly, there is  no relationship  or  no correlation  between the variables.
  ::如果散射图上的点似乎随机分散,则变量之间没有任何关系或相关性。

  播放段落

  When there is a positive or negative relationship between your variables, you can draw a  line of best fit . This is a line that will not go through every point on the scatter plot, but will show the general trend of your data.
  ::当变量之间存在正或负关系时,您可以绘制一条最合适的线条。这条线条不会穿透分布图上的每一个点,而是会显示数据的一般趋势。

  播放段落

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

  播放段落

  A teacher wants to know if there is a relationship between the amount of time her students spent working on a social studies report and the grade each student received. She surveyed 10 students and recorded the data below.
  ::教师想知道,她的学生在社会研究报告上花费的时间与每个学生获得的年级之间是否有关系,她对10名学生进行了调查,记录了以下数据。

  Data for Hours Worked and Grade on Report

  Student	Number of Hours Worked	Grade
  Ahmad	5	90
  Becky	3	80
  Darrell	3.5	80
  Emma	1	60
  Guillermo	4.5	90
  Helene	1	70
  Kiet	3	75
  Nykeisha	4	85
  Ollie	2	70
  Zivia	2.5	75

  播放段落
  1. Make a scatter plot based on the data.
     ::根据数据绘制散射图 。
  播放段落
  2. Determine if there is a relationship between the number of hours worked and the grade received. If so, describe the relationship.
     ::确定工作小时数和收到的职等之间是否有关系。如果有关系,请说明关系。
  播放段落
  3. Suppose an eleventh student spent 1.5 hours working on her report. Based on the scatter plot, predict the grade you would expect her to receive.
     ::假设第11个学生花了1.5小时去写她的报告。根据散射图,预测你期望她得到的分数。

  播放段落

  Let's start by looking at part a.
  ::我们先看看A部分

  播放段落

  To make the scatter plot you need to first scale your axes. The teacher wants to know if the number of hours worked is related to the grade a student earned, so use the horizontal axis of the scatter plot to show the number of hours worked. Notice that in the table, the number of hours worked ranges from 1 to 5, so draw your horizontal axis so it goes from 0 to 6.
  ::要绘制散射图, 您需要首先缩放您的斧头。 老师想知道工作小时数是否与学生所得的年级有关, 所以使用散射图的水平轴显示工作小时数 。 请注意, 在表格中, 工作小时数介于 1 到 5 之间, 请绘制您的水平轴, 从 0 到 6 。

  播放段落

  Next, scale the vertical axis. You will use the vertical axis to show the grades students received. The grades in the table  range  from 60 to 90. Showing every grade from 0 to 100 would make the plot very large, so include a break in the axis between 0 and 60. Use intervals of 10 for the rest of scale.
  ::接下来, 缩放垂直轴。 您将使用垂直轴显示学生的成绩。 表中的年级从60到90不等, 显示每个年级从0到100, 会让这个图块变得非常大, 所以包括一个在0到60之间断开轴线的间距。 其余的缩放间隔为 10 。

  播放段落

  Now, you can plot a point for each pair of data in the table. For example, Ahmad worked for 5 hours and earned a grade of 90. So, plot a point at (5, 90) on the scatter plot. Do this until you have plotted all 10 data points.
  ::现在, 您可以为表格中的每对数据绘制一个点。 例如, Ahmad 工作了 5 小时, 挣到了90 级。 所以, 请在 散射 地块上绘制一个点( 5 , 90 ) 。 在绘制所有 10 个数据点之前, 这样做 。

  播放段落

  The answer to part a is shown below.
  ::对A部分的答复如下。

  

  [Figure 4]

  播放段落

  Next let's look at part b.
  ::接下来让我们看看B部分。

  播放段落

  Notice that when you look at the scatter plot the points seem to form a line going up from left to right. You could sketch in a potential line of best fit that shows this general trend of the data.
  ::请注意, 当您查看散射图时, 点似乎形成一条从左向右的线条。 您可以绘制一个最合适的可能线条, 显示数据的一般趋势 。

  

  [Figure 5]

  播放段落

  The answer is that because the line of best fit slants up from left to right, this scatter plot shows a positive relationship between hours worked and grade on the report. This means that in general, the longer a student spent working on the report, the higher the student's grade on the report.
  ::答案是,由于最合适的倾斜线从左向右倾斜,这一散射图显示了工作时数与报告分数之间的积极关系。 这意味着,一般来说,学生在报告上花费的时间越长,报告的学生分数越高。

  播放段落

  Last let's look at part c.
  ::最后让我们看看C部分

  播放段落

  Because the scatter plot shows a relationship between hours worked on the report and grade on the report, you can use the scatter plot to make predictions for other values within the original range of your data.
  ::由于散射图显示了报告工作小时与报告等级之间的关系,您可以使用散射图预测原始数据范围内的其他数值。

  播放段落

  None of the original ten students worked only 1.5 hours on the report; however, you can assume that this student would fit into the trends seen with the rest of the students.
  ::最初的10名学生中没有一个只根据报告工作1.5小时;然而,你可以假定,该学生符合其他学生所看到的趋势。

  播放段落

  Look at the scatter plot with the line of best fit. Find 1.5 hours on the  $\begin{array}{r}x\end{array}$ -axis and move up until you hit the line of best fit. You are at a height corresponding to a grade of 65 on the report. This means that if a student only worked 1.5 hours on the report, you can predict that they will get a 65 as a grade on the report.
  ::查看最合适的分布图 。 在 x - 轴上找到1.5 小时, 并移动到最合适的线上 。 您处于报告65 年级的高度 。 这意味着如果学生在报告上只工作1.5 小时, 您可以预测他们在报告上会得到65 年级的成绩 。

  播放段落

  The answer is that you predict that a student who only worked 1.5 hours on the report will receive a grade of a 65 on the report.
  ::答案是,你预测,在报告上只工作1.5小时的学生,在报告上将获得65年级的成绩。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about William, who was researching global warming.
  ::早些时候,你得到一个问题 威廉,谁是研究 全球变暖。

  播放段落

  He found a scatter plot that showed the annual average global temperature each year since 1880.
  ::他发现一个散射地块,显示自1880年以来每年全球平均气温。

  

  [Figure 6]

  播放段落

  In order to determine if the graph shows any correlation, William should look to see if there is a pattern in the scatter plot. Notice that when you look at the scatter plot overall the points seem to form a line going up from left to right. While there are brief periods where the points head back down, the overall trend is up. This means that there is a positive correlation.
  ::为了确定图表是否显示任何关联性, William应该查看散射图中是否有图案。 请注意, 当您查看散射图时, 这些点似乎形成一条从左向右的线条。 虽然有点向下退的短暂时期, 但总的趋势却在上升。 这意味着正相关关系。

  播放段落

  The answer is that the scatter plot shows a positive correlation between year and annual average global temperature.
  ::答案是,散射图显示年与年平均全球温度之间的正相关关系。

  播放段落

  This means that the average annual global temperature appears to be going up over time. Keep in mind the scale on the vertical axis. The annual average global temperature has only changed  $\begin{array}{r}{1}^{\circ }C\end{array}$  over 120+ years so while there is definitely a positive correlation, it's not quite as drastic as it might appear on the scatter plot.
  ::这意味着全球平均年温度似乎会随着时间而上升。 记住垂直轴的尺度。 全球平均年平均温度在120年以上仅改变了1 °C, 所以在肯定有正相关关系的情况下, 它并没有在散射图上出现那么剧烈。

  播放段落

  Example 2
  ::例2

  播放段落

  Look at the following set of ordered pairs. Would the scatter plot show a positive correlation, a negative correlation or no correlation?
  ::看看下面的一组定购配对。 散射图显示正相关、 负相关或无相关吗 ?

  $\begin{array}{r}(1,2),(3,5),(7,10),(9,15),(4,8)\end{array}$

  播放段落

  First, plot all five points on a graph.
  ::首先,在图表上绘制所有五个点。

  

  [Figure 7]

  播放段落

  Next, look to see if there is a pattern in the graph. Notice that when you look at the scatter plot the points seem to form a line going up from left to right. This means that there is a positive correlation between the  $\begin{array}{r}x\end{array}$ -coordinates and the  $\begin{array}{r}y\end{array}$ -coordinates.
  ::下一步, 看看图中是否有图案。 请注意, 当您查看分布图时, 点似乎形成一条从左向右的线条。 这意味着 x - 坐标和 y - 坐标之间有正相关关系 。

  播放段落

  The answer is that the scatter plot shows a positive correlation.
  ::答案是,散射图显示出正相关关系。

  播放段落

  Example 3
  ::例3

  播放段落

  Does a line of best fit on a plot with a positive correlation go up or down as you move from left to right on the scatter plot?
  ::在分布图上从左向右移动时, 与正相关联的地块上是否最适合的线向上或向下移动?

  播放段落

  This is something that you have to remember. Positive correlation means that as the first  variable  increases, the second variable increases as well. This corresponds to points (and a line of best fit) that move up as you go from left to right.
  ::这是你必须记住的。正相关意味着随着第一个变量的增加,第二个变量也随之增加。这与在从左向右移动时向上移动的点(和最合适的线)相对应。

  播放段落

  Negative correlation would mean that as one variable increases, the second variable decreases. Negative correlation corresponds to points that move down as you go from left to right on your scatter plot.
  ::负相关性将意味着,随着一个变量的增加,第二个变量就会减少。负相关性与分布图上从左向右移动的点相对应。

  播放段落

  The answer is that the line of best fit on a scatter plot with positive correlation will go up as you move from left to right.
  ::答案是,在从左向右移动时, 与正相关联的散射地块上的最佳匹配线将会上升。

  播放段落

  Example 4
  ::例4

  播放段落

  Look at the following set of ordered pairs. Would the scatter plot show a positive correlation, a negative correlation or no correlation?
  ::看看下面的一组定购配对。 散射图显示正相关、 负相关或无相关吗 ?

  $\begin{array}{r}(1,12),(5,5),(3,8),(9,1),(8,4)\end{array}$

  播放段落

  First, plot all five points on a graph.
  ::首先,在图表上绘制所有五个点。

  

  [Figure 8]

  播放段落

  Next, look to see if there is a pattern in the graph. Notice that when you look at the scatter plot the points seem to form a line going down from left to right. This means that there is a negative correlation between the  $\begin{array}{r}x\end{array}$ -coordinates and the  $\begin{array}{r}y\end{array}$ -coordinates.
  ::下一步, 看看图中是否有图案。 请注意, 当您查看分布图时, 点似乎形成一条从左向右的线条。 这意味着 x - 坐标和 y - 坐标之间存在负相关关系 。

  播放段落

  The answer is that the scatter plot shows a negative correlation.
  ::答案是散射图显示出负相关关系。

  播放段落

  Example 5
  ::例5

  播放段落

  Look at the following set of ordered pairs. Would the scatter plot show a positive correlation,  a negative correlation or no correlation?
  ::看看下面的一组定购配对。 散射图显示正相关、 负相关或无相关吗 ?

  $\begin{array}{r}(1,12),(8,9),(3,10),(2,4),(5,2),(6,6)\end{array}$

  播放段落

  First, plot all six points on a graph.
  ::首先,在图表上绘制所有六点图。

  

  [Figure 9]

  播放段落

  Next, look to see if there is a pattern in the graph. Notice that when you look at the scatter plot there does not seem to be any real pattern to the points. The points don't seem to be trending up or down. This means that there is no correlation between the  $\begin{array}{r}x\end{array}$ -coordinates and the  $\begin{array}{r}y\end{array}$ -coordinates.
  ::下一步, 看看图中是否有图案。 注意当您查看分布图时, 点的图案似乎没有真实的图案。 点似乎没有向上或向下移动。 这意味着 x - 坐标和 y - 坐标之间没有关联 。

  播放段落

  The answer is that the scatter plot shows no correlation.
  ::答案是,散射图显示没有相关性。

  播放段落

  Review
  ::回顾

  播放段落

  This scatter plot shows the relationship between the last digit of ten students’ phone numbers and their vocabulary quiz scores.
  ::这个散射图显示了十位学生最后一位数的电话号码与他们的词汇测验分数之间的关系。

  

  [Figure 10]

  播放段落
  1. Does this scatter plot show a positive relationship, a negative relationship, or no relationship?
     ::这块分散的地块是否显示正关系, 负关系,还是没有关系?
  播放段落
  2. How many students have a six as the last digit in their phone number?
     ::有多少学生的电话号码中 6是最后一位数?
  播放段落
  3. How many students have an eight as the last digit?
     ::有多少学生的8是最后一位数?
  播放段落
  4. How many students received a grade of 70%?
     ::有多少学生获得70%的年级?
  播放段落
  5. How many students received a grade of 60%
     ::有多少学生获得60%的年级
  播放段落
  6. How many students earned 100%?
     ::有多少学生挣100%?
  播放段落
  7. How many students earned a 75%?
     ::有多少学生挣75%?
  播放段落
  8. True or false. No one earned below a 60%.
     ::不管是真还是假 没有人的收入低于60%
  播放段落
  9. True or false. No one earned an 80%.
     ::不管是真实的还是假的 没人挣到百分之八十
  播放段落
  10. True or false. No one earned an 85%.
      ::不管是真还是假 没人挣85%

  播放段落

  Serena wants to know if there is a relationship between a person’s age and the number of DVDs they purchased in one year. She surveyed a group of people and recorded the data in the table below.
  ::Serena想知道一个人的年龄和他们在一年中购买的DVD数量之间是否有关系。 她对一群人进行了调查,并在下表中记录了数据。

  Person	Age	Number of DVDs Purchased
  Person 1	18	14
  Person 2	19	13
  Person 3	20	13
  Person 4	20	12
  Person 5	21	11
  Person 6	22	12
  Person 7	22	11
  Person 8	23	10
  Person 9	24	9
  Person 10	25	9

  播放段落
  11. Make a scatterplot for the data in the table.
      
      Use the scatterplot you made from Serena's data in the question above to answer the following questions:
      ::为表格中的数据绘制一个散射图。使用您根据Serena在上述问题中的数据制作的散射图回答下列问题:
  播放段落
  12. True or false. The scatter plot shows a negative correlation.
      ::散射图显示的是负相关关系。
  播放段落
  13. True or false. The scatter plot shows no correlation.
      ::无论是真实的还是虚假的。 散射图显示没有关联性 。
  播放段落
  14. True or false. The scatter plot shows a positive correlation.
      ::散射图显示正相关关系。
  播放段落
  15. If the trend in the scatter plot continues, predict the number of DVDs you would expect a 27-year-old person to buy in one year.
      ::如果散射地块的趋势继续下去, 预测DVD数量, 你会期待一个27岁的人在一年内购买DVD。

  播放段落

  Review (Answers)
  ::回顾(答复)