章节大纲

  • 常规

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  • 平均值、中值、模式和范围

    Candy Yum-Yums!
    ::甜甜的尤姆斯糖!

    Joel, Annie, David and Sara each received a bag of candy containing different numbers of candy pieces. Use the interactive below to divide all the candy pieces equally between them.
    ::乔尔、安妮、大卫和莎拉每人都收到一袋糖果,里面装有不同数量的糖果。用下面的交互方式,将所有糖果都平分。

     

     

     

     

    A measure of center is a single number used to describe a set of numeric data . It describes a typical value from the data set . Measures of center include the mean and the .
    ::中心测量是用于描述一组数字数据的单个数字。它描述数据集的典型值。中心测量包括平均值和 。

    The mean (or what is more commonly referred to as the average) of a data set is the sum of the data values divided by the number of data values in the set. As you saw in the warm-up, the mean can be thought of as "evening out" the data values.
    ::数据集的平均值( 或更常见的称为平均值) 是数据值除以集中数据值数的总和。 正如您在热身中看到的那样, 平均值可以被视为“ 平衡” 数据值 。

    The range is a measure of spread. You can find the range by taking the greatest data value and subtracting the least data value. In other words, it is the difference between the maximum and minimum data point.
    ::范围是扩展的量度。您可以通过使用最大数据值和减去最小数据值来找到范围。换句话说,它是最大数据点和最小数据点之间的差别。

    Example
    ::示例示例示例示例

    Find the mean and range for the number of yards gained by Roger during his seven carries in the football game: {2, 6, 20, 11, 8, 12, 4}.
    ::找到罗杰在足球比赛中 7次飞行中 赢得的码数的平均值和范围 : {2,6,20,11,8,12,4}

    To find the mean, add up the number of yards for Roger's seven carries and divide the total by 7.
    ::加上罗杰的七架马车的开场数 将总数除以7

    Mean = 2 + 6 + 20 + 11 + 8 + 12 + 4 7 = 63 7 = 9

    ::平均值=2+6+20+11+8+12+47=637=9

    To find the range, identify the greatest and least value in the data set. The greatest value is 20 and the least value is 2. 
    ::要找到范围, 请在数据集中指定最大值和最小值。 最大值为 20, 最小值为 2 。

    Range = 20 − 2 = 18
      
    ::范围=20-2=18

     

    Text, "Hello, Mean!"
    ::文字,"你好,坏人!"

    Have you ever wondered how a baseball player's batting average is calculated? Or how a miles-per-gallon (mpg) average for a car is calculated? Take a look further into this activity...
    ::你有没有想过棒球运动员的击球平均速率是如何计算的?或者汽车的每加仑平均速率是如何计算的?更深入地研究这一活动...

    Several students in Malikai's class were randomly selected to participate in a study about the number of text messages they sent yesterday. Their answers were as follows: 1, 0, 10, 7, 13, 2, 9, 15, 3, 0.
    ::在Malikai的班级中,有几名学生被随机挑选参加关于昨天发送的短信数量的研究,其答复如下:1,0,10,7,13,2,9,15,3,0。

    Use the interactive below to learn how to calculate the mean of the data set above.
    ::使用下面的交互式数据来学习如何计算上述数据集的平均值。

     

     

     

     

    Discussion Question
    ::讨论问题

    Celina claims that if a dataset contains only one repeated number, that number will be the mean of the set. Do you agree of with Celina's claim? Use evidence to support your argument.
    ::Celina声称,如果数据集只包含一个重复的数字,该数字将是集的平均值。您同意Celina的索赔吗?使用证据支持你的论点。

     

    Mind the Median!
    ::注意中音!

    The median represents the middle value of an ordered data set. It is another measure of center. You might have heard of the word "median" before to describe the strip of land in the center of a roadway that separates the lanes of traffic going in opposite directions. Just like a median divides a road down the middle, in statistics , the median divides or splits a data set down the middle into two data sets.
    ::中位数代表了定购数据集的中间值。 这是中心的另一个度量。 您可能听说过“ 中位数 ” 这个词, 以描述路中央的地带, 这条路将交通道向相反方向分隔开来。 就像中位数分割了中间道路一样, 在统计方面, 中位数分割或将中位数划分为两个数据集。

    Example
    ::示例示例示例示例

    lesson content

    A coach records the distances that some cross-country team athletes ran last week (in miles): {3, 5, 10, 4, 7, 7, 8, 1, 3, 9, 8}
    ::教练记录一些跨国球队运动员上周的距离(英里):{3,5,10,4,7,7,7,7,8,1,3,3,9,8}

    Use the interactive below to learn how to calculate the median of the data set above.
    ::使用下面的交互式数据来学习如何计算上述数据集的中位数。

     

     

     

     

    In the last question, the students' test scores had two values in the middle. Recall that the original data set was: {87, 90, 77, 83, 99, 94, 93, 90, 85, 83}. How many data values are there?
    ::在最后一个问题中,学生考试分数中间有两个值。 回顾原始数据集是 {87, 90, 77, 83, 99, 94, 93, 90, 85, 83}。 有多少数据值?

    Whenever a data set has an even number of data points, there will be two middle values. The steps below describe the process for finding the median when there are two middle values:
    ::当数据集有偶数的数据点时,将有两个中间值。以下步骤描述在有两个中间值时找到中位数的过程:

    1. Order the values in this data set from least to greatest: 77, 83, 83, 85, 87, 90, 90, 93, 94, 99
      ::将该数据集中的数值从至少排列到最大:77、83、83、85、87、90、90、93、94、99
    2. Identify the two middle values: 87 and 90
      ::确定两个中间值:87和90
    3. Find the (mean) average of these two middle values:
      ::查找这两个中间值的平均(平均值) :

    Median = 87 + 90 2 = 88.5

    ::中位数=87+902=88.5

     

    Use the following interactive to practice finding the mean.
    ::使用以下互动手段来实际寻找平均值。

     

    Mode Your Most! 
    ::你最喜欢的模式!

    The mode is the number or data value that occurs most frequently in the data set. A data set can contain multiple modes as long as they have the same frequency. For instance, if there are two data values in the set with the same highest frequency (say, they each appear five times) then this data set is said to be " bimodal ." If there are more than two modes in a data set then it is considered "multi-modal."
    ::模式是数据集中最常出现的数字或数据值。 数据集可以包含多个模式, 只要它们具有相同的频率。 例如, 如果数据集中有两个数据值, 其最高频率相同( 比如, 每个数据值显示五倍) , 那么该数据集就被称为“ 双元 ” 。 如果数据集中有两个以上模式, 那么它就被认为是“ 多模式 ” 。

    Use the interactive below to practice finding the mode.
    ::使用下面的交互方式来练习寻找模式 。

     

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. How can you use measures of center to describe a data set?
      ::您如何使用中心测量来描述数据集 ?
    2. When ordering a set of data, must you list numbers that repeat?
      ::当命令一组数据时, 您必须列出重复的数字 ?
    3. How will data values that are unusually large or small (remember, outliers ?) compared to the rest of the data affect the mean average?
      ::与其他数据相比异常大或小的数据值(记得,离子体? )如何影响平均数?

     

       Summary
    ::摘要

    • A data set with an even number of values will have two middle numbers. You need to find the average of those two values to get the median.
      ::具有偶数数值的数据集将有两个中位数。 您需要找到这两个值的平均值才能获得中位数 。
    • A single outlier commonly affects the mean more than the median or the mode.
      ::单极点通常对平均值的影响大于中位数或模式。
    • Data with two modes is called 'bimodal'. Data with three or more modes is 'multi-modal'.
      ::有两种模式的数据被称为“ 双模式 ” 。 有三种或三种以上模式的数据是“ 多模式 ” 。