10.7 使用MAD-interactive

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  使用 MAD

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  Which Chickens Eat Better?
  ::哪个鸡吃得更好?

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  A chicken farmer wants her chickens to all have about the same weight. Sh e is trying two types of feed to  see which type produces the best results. All the chickens in Pen A are fed Premium Growth feed, and all the chickens in Pen B are fed Maximum Growth feed. The farmer records the weights of the chickens in each pen in the tables below.
  ::养鸡者希望鸡的重量与养鸡的重量大致相同。 她正在尝试两种喂养方式,以检验哪种喂养方式产生最佳效果。 在Pen A中,所有的鸡都被喂养了Premium Ecreat 饲料,而在Pen B中,所有的鸡都被喂养了最大生长饲料。 农民在下面的表格中记录了每只养鸡的重量。

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  Which chicken feed produces   less variability   in weight?
  ::哪种鸡饲料的重量变化性较小?

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  $$\begin{align*}\large{\text{Pen A: }} & \large{\text{Premium Growth Weights (lbs.)}}\\ &\large{\begin{array}5.8 & 6.1 & 5.5 & 6.6 & 7.3 \\ 5.9 & 6.3 & 5.7 & 6.8 & 7.1\end{array}}\\ \ \\ \large{\text{Pen B: }} & \large{\text{Maximum Growth Weights (lbs.)}}\\ &\large{\begin{array}7.7 & 7.4 & 5.4 & 7.8 & 6.1 \\ 5.2 & 7.5 & 7.9 & 6.3 & 5.6\end{array}}\\\end{align*}$$
  ::Pen A: 倍增重量(磅) 86.15.56.67.35 96.35.76.87.1 Pen B: 最大增长重量(磅) 77.45.47.86.15.27.57.35.6

   

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  1.

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  Look at the weights for both data sets. Find the mean weight for Pen A and Pen B.
  ::查看两个数据集的重量。 查找 Pen A 和 Pen B 的平均重量 。

  Select all that apply

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  The mean weight of the chickens in Pen A is about 6.2 pounds.
  ::在Pen A的鸡平均体重约为6.2磅。

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  The mean weight of the chickens in Pen B is about 6.9.
  ::Pen B 中鸡的平均重量约为6.9。

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  The mean weight of the chickens in Pen B is about 6.0 pounds.
  ::Pen B 鸡的平均重量约为6.0磅。

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  The mean weight of the chickens in Pen A is about 5.8 pounds.
  ::在Pen A的鸡平均体重约为5.8磅。

   

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  A  measure of variability is a single number used to describe the spread of a data set . It can also be called a measure of spread. 
  ::量度变异性是用来描述数据集分布的单一数字,也可以称为量度扩展。

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  The mean absolute deviation  is an example of another measure of variability. It is the  average of the distances between  each data value and the mean of the data set.
  ::绝对偏差是另一种可变度的一个例子,是每个数据值与数据集平均值之间的平均距离。

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  The mean absolute deviation, or MAD, is useful for answering about the real world. Many of these questions may have implications for the operation of various businesses.
  ::绝对偏差,或者说MAD,对于回答真实世界来说是有用的。 其中许多问题可能会对各种企业的经营产生影响。

   

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  Jenna's Math Homework Problems
  ::Jenna的数学家庭工作问题

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  Over a two-week period, Jenna had the following number of math homework problems given each day: 
  ::Jenna每天有下列数学作业问题:

  $$\begin{align*}\large{\text{[20, 0, 7, 10, 1, 11, 0, 25, 15, 1]}}\end{align*}$$

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  From this data, you can determine that Jenna's mean number of homework problems was 9 per day. What is the mean absolute deviation for the number of homework problems?
  ::从这些数据中,你可以确定Jenna的平均功课问题数量是每天9个。功课问题数量的绝对偏差是多少?

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  Use the interactive below to calculate the MAD for the number of homework problems Jenna has per day. What can you say about the deviation in how many problems she is assigned from day to day?
  ::Jenna每天有多少家庭作业问题,请使用下面的交互数据来计算MAD。您能对她每天分配多少家庭作业问题的偏差怎么说?

   

   

   

   

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  Discussion Question
  ::讨论问题

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  Suppose a data set contains all whole numbers. Would the MAD for the data set also be a whole number? Explain.
  ::假设数据集包含全部数字。 数据集的 MAD 是否也是整数? 解释 。

    

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  Frank's Study 
  ::弗兰克的研究

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  Frank wants to know how many people live in each household in his town. He conducts a random survey of 10 people and asks how many people live in their household. His results are :
  ::他对10人进行了随机调查,并询问有多少人生活在他们的家庭中。

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  $$\begin{align*}\large{\text{Nu}} & \large{\text{mber of People per Household}}\\ & \large{1, ~6, ~2, ~4, ~4, ~3, ~5, ~5, ~2, ~8}\\\end{align*}$$
  ::1、6、2、4、4、4、3、5、5、5、2、8

   

   

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  Discussion Question
  ::讨论问题

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  Each of the values in a data set is increased by 10. Esteban believes that this will increase the MAD of the dataset because the values are greater. Evan believes that the mean will remain the same. Who do you believe is correct? Support your answer with evidence.
  ::Esteban认为,这将增加数据集的MAD值,因为数值更大。 Evan认为,平均值将保持不变。你认为谁是正确的?用证据支持你的答复。

    

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  Yo-yogurt! 
  ::Yo -yogurt! 哟 -yogurt! 哟 -yogurt! 哟 -yogurt! 哟 -yo -yogurt!

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  Each yogurt treat served at a frozen yogurt shop must be the same size. A new worker spends his first week on the job learning to serve the correct amount. The tables show the sizes of 10 yogurt treats the worker served at the beginning of his first week, and 10 yogurt treats he served at the end of his first week. 
  ::冷冻酸奶店的每个酸奶待遇必须大小相同。 一名新工人在工作上花一周时间学习,以达到正确的数量。 表格显示工人在第一周开始时的10个酸奶待遇大小,第一周结束时的10个酸奶待遇。

  Serving Sizes (grams) at Beginning of Week 1

  76

  81

  85

  79

  89

  86

  84

  80

  88

  79

  Serving Sizes (grams) at End of Week 1

  79

  82

  84

  81

  77

  85

  82

  80

  78

  83

   

   

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  Discussion Questions:
  ::讨论问题:

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  1. How could you explain the difference in MADs from the beginning of week 1 to the end of week 1?
     ::从第1周开始到第1周结束,你如何解释MADs的差别?
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  2. How can you use the MADs from various data sets to compare the data sets?
     ::您如何使用来自不同数据集的 MAD 来比较数据集?

  Summary

  播放段落 A measure of variability is a number that is used to describe the spread of a data set. ::衡量可变性的尺度是用来描述数据集分布的数字。 播放段落 The mean absolute deviation (MAD) is the measure of variability that is used to measure how spread out the values in the data set are. ::平均绝对偏差(MAD)是用于衡量数据集中数值分布方式的可变性度。