11.1 平均值

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  平均平均

  

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  This summer, Marco will wash cars five days a week to earn some money. He has worked one week already. Marco washed three cars on Wednesday, one car on Thursday, four cars on Friday, five cars on Saturday and two cars on Sunday. Marco gets paid $5 for every car he washes, and wants to know how much money he will have after eight weeks. Marco thinks he can wash the same average number of cars each week. How can Marco figure out how much money he will earn in total?
  ::今年夏天,马可将每周洗车五天以赚取一些钱。他已经工作了一个星期。马尔科在星期三洗了三辆汽车,在星期四洗了一辆车,在星期五洗四辆车,在星期六洗五辆汽车,在星期天洗两辆汽车。马科每次洗车都得到五美元,并想知道八周后他有多少钱。马科认为他可以每周洗同样的平均车数。马科怎么知道他能挣多少钱?

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  In this concept, you will learn how to calculate mean.
  ::在这个概念中,你会学会如何计算意思。

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  Calculating Mean
  ::计算平均值

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  Data is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept we will analyze numerical data using the mean.
  ::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。在这个概念中,我们将使用平均值分析数字数据。

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  Mean is a numerical value that measures the spread of a data set . The mean is one way to determine the central or typical value of the set. Mean is also called the average.
  ::平均值是衡量数据集分布的数值。平均值是确定数据集中心值或典型值的一种方法。平均值也称为平均值。

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  To calculate the mean, first sum the data values in the set and then divide by the number of values in the set.
  ::要计算平均值,首先将数据集中的数据值相加,然后除以数据集中的数值数。

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

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  Find the mean for the set of data: 47, 56, 51, 45, and 41.
  ::查找数据集的平均值:47、56、51、45和41。

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  First, add the data values to calculate the sum.
  ::首先,添加数据值来计算总和。

  $$\begin{array}{r}47+56+51+45+41=240\end{array}$$

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  Second, divide the sum by the number of values in the set. Since there are five values in the data set, you will divide by 5.
  ::第二,将总和除以集中的值数。由于数据集中有5个值,所以将除以5。

  $$\begin{array}{r}240÷5=48\end{array}$$

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  The answer is the mean is 48.
  ::答案是48岁

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Marco and his dirty cars.
  ::之前,你得到一个问题 关于马可和他的脏车。

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  This summer, Marco is washing cars 5 days a week to earn money. Marco has kept track of the number of cars he washed in the first week. These values are his data. Marco organized his data in the following table.
  ::今年夏天,马可每周5天洗车挣钱。马可记录了第一周洗车数量。这些是他的数据。马科在下一张表格中整理了他的数据。

  Marco's Car Wash

  Day	Number of Cars Washed
  Wednesday	3
  Thursday	1
  Friday	4
  Saturday	5
  Sunday	2

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  Marco wants to know how much money he will have after 8 weeks of washing cars. Marco gets paid $5 for each car he washes. If Marco washes the same average number of cars each week, how much money will he earn?
  ::Marco想知道在洗车8周后他有多少钱。 Marco每次洗车都要5美元。如果Marco每周洗的汽车平均数量相同,他能挣多少钱?

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  First, find the average number of cars washed in the first week. Then, use the average to calculate how much money Marco will earn.
  ::首先,找到第一周洗车的平均数量。然后,用平均数量来计算Marco将赚多少钱。

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  To find the average number of cars Marco washed in the first week, add the number of cars washed.
  ::为了发现第一周Marco被洗的汽车的平均数量,加上被洗的汽车数量。

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  $$\begin{array}{r}3+1+4+5+2=15\end{array}$$

  
  Next, divide by the number of days, 5.
  ::3+1+4+5+2=15 下一个除以天数,5。

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  $$\begin{array}{r}15÷5=3\end{array}$$

   
  The average number of cars Marco washed in a day is 3.
  ::155=3 马可每天洗的汽车平均数量为3辆。

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  Next, calculate the average number of cars Marco washes in a week. Since Marco works 5 days a week, multiply 3 (the average number of cars washed per day) by 5 (days worked in a week).
  ::接下来计算一周内马可洗车的平均数量。 自从马可每周工作5天,每星期工作5天,乘以3(每天洗车的平均数量)乘以5(每周工作1天)。

  $$\begin{array}{r}3\times 5=15\end{array}$$

  
  

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  The average number of cars Marco washes in a week is 15.
  ::一周内马可洗车的平均数量为15辆。

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  Next, calculate the average number of cars Marco will wash in 8 weeks. To do this, multiply 15 (average number of cars washed per week) by 8 (number of weeks worked).   
  ::接下来,计算Marco在8周内洗车的平均数量。为此,将15次(每周洗车的平均数量)乘以8次(工作周数)乘以15次(每周洗车的平均数量)乘以8次(工作周数)。

  $$\begin{array}{r}15\times 8=120\end{array}$$

   

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  The average number of cars Marco will wash in 8 weeks is 120.
  ::Marco在8周内洗车的平均数量是120辆。

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  Next, calculate how much money Marco will make in 8 weeks. To do this, multiply 120 (average number of cars washed in 8 weeks) by $5 (amount earned per car washed).
  ::接下来,请计算马可在8周内赚到多少钱。 为此,请将120美元(8周内洗车的平均数量)乘以5美元(每洗车挣得的金额)乘以5美元(每洗车挣得的金额 ) 。

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  $$\begin{array}{r}1200\times 8=600\end{array}$$

  
  The answer is Marco will earn $600.
  ::1200x8=600 答案是马可会赚600美元

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  Example 2
  ::例2

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  West Elementary School has four classes of fifth grade students. Mr. Hernandez has 23 students, Mrs. Johnson has 26 students, Ms. Ruiz has 25 students, and Mr. Smith has 21. What is the average number of fifth grade students in each class?
  ::西小学有4个五年级学生班,Hernandez先生有23名学生,Johnson女士有26名学生,Ruiz女士有25名学生,Smith先生有21名学生,每个班的平均五年级学生人数是多少?

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  Remember that to calculate the average is the same as calculating the mean. You must follow the same steps. First, find the sum of the fifth grade students. To do this, add the number of students in each class.
  ::记住计算平均值与计算平均值相同。 您必须遵循相同的步骤。 首先, 找到五年级学生的总和。 要做到这一点, 增加每个班的学生人数 。

  $$\begin{array}{r}24+26+25+21=96\end{array}$$

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  Next, divide by the number of classes. In this case there are 4 classes.
  ::其次,除以班级数量。在这种情况下,有4个班级。

  $$\begin{array}{r}96÷4=24\end{array}$$

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  The answer is the average number of fifth grade students in each class is 24.
  ::答案是每班五年级学生的平均人数为24人。

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  Example 3
  ::例3

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  Find the average of the following data set.
  ::查找下列数据集的平均值。

  $$\begin{array}{r}11,13,13,15,16,22,24,25,30,32\end{array}$$

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  First, add the values.
  ::首先,添加值。

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  $$\begin{array}{r}11+13+14+15+16+22+24+25+30+32=202\end{array}$$

   
  Second, divide by the number of values in the set. In this set there are 10, so divide by 10. 
  ::11+13+14+14+15+16+22+24+25+30+32=202 第二,除以数据集中的值数。在此组中,有10个,因此除以10。

  $$\begin{array}{r}202÷10=20.2\end{array}$$

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  This average in this set is 20.2. The average, or mean, is not always a whole number.
  The answer is the average is 20.2.
  ::这一组的平均数为20.2。平均值或平均值并不总是一个整数。答案是平均数为20.2。

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  Example 4
  ::例4

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  John wants to know his average quiz grade based on the following quiz scores.
  ::约翰想知道他的平均测验成绩 根据以下的测验分数

  $$\begin{array}{r}78,90,83,88,67,90,84,69,56\end{array}$$

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  First, add the values.
  ::首先,添加值。

  $$\begin{array}{r}78+90+83+88+67+90+84+69+56=705\end{array}$$

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  Second, divide the sum by the number of values in the set. In this set there are 9, so you divide by 9. 
  ::第二,将总和除以集中的值数。在这个组中,9是9,所以将9除以9。

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  $$\begin{array}{r}705÷9=\mathrm{78.3...}\approx 78.3\end{array}$$

  
  
  Notice the average, or mean, is not a whole number. In this problem, round the answer to the nearest tenth. 
  The answer is John's average quiz grade is 78.3.
  ::7059=78.3... 78.3 注意平均值或平均值不是一个整数。 在此问题上, 将答案四舍五入到最近的十分。 答案是约翰的平均测验等级为78.3。

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  Example 5
  ::例5

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  The chart below shows the daily temperature in San Diego for the first seven days in August. Calculate the mean temperature.
  ::下表显示圣地亚哥8月份头七天的每日温度。计算平均温度。

  Daily Temperatures for August

  Date	Temperature ( $\begin{array}{r}{}^o\end{array}$ F)
  Sunday 8/1	88
  Monday 8/2	83
  Tuesday 8/3	87
  Wednesday 8/4	89
  Thursday 8/5	82
  Friday 8/6	79
  Saturday 8/7	87

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  First, calculate the sum of the data values.
  ::首先,计算数据值的总和。

  $$\begin{array}{r}88+83+87+89+82+79+87=595\end{array}$$

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  Second, divide the sum by the number of data values in the set. Since there are seven values in this set, you will divide by 7.
  ::第二,以数据集中的数据值数除以总和。由于此集中有7个值,您将除以7。

  $$\begin{array}{r}595÷7=85\end{array}$$

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  The answer is the mean temperature for the first week in August was $\begin{array}{r}{85}^{o}F\end{array}$ .
  ::答案是8月第一周的平均温度是85摄氏度。

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  Review
  ::回顾

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  Find the mean for each set of data. Round to the nearest hundredth when necessary.
  ::查找每组数据的平均值。 必要时, 圆到最接近的第一百位 。

  1. 4, 5, 4, 5, 3, 3, 6, 7, 8
  2. 6, 7, 8, 3, 2, 4, 9, 10, 11, 12
  3. 11, 10, 9, 13, 14, 16, 20, 22, 22
  4. 21, 23, 25, 22, 22, 27, 18, 20
  5. 27, 29, 29, 32, 30, 32, 31
  6. 34, 35, 34, 37, 38, 39, 39
  7. 43, 44, 43, 46, 39, 50
  8. 122, 100, 134, 156, 144, 110, 120, 123, 130
  9. 224, 222, 220, 222, 224, 224
  10. 540, 542, 544, 550, 548, 547
  11. 762, 890, 900, 789, 780, 645, 700
  12. 300, 400, 342, 345, 403, 302
  13. 200, 199, 203, 255, 245, 230, 211
  14. 1009, 1000, 1200, 1209, 1208, 1217
  15. 2300, 2456, 2341, 2400, 2541, 2321

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  Review (Answers)
  ::回顾(答复)

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  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 。

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  Resources
  ::资源