章节大纲

  • 常规

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  • 描述性统计

    Four girls of varying heights are standing outdoors, smiling and interacting.

    The girls in this picture vary in height. The shortest girl has a height of 52 cm, and the tallest girl has a height of 64 cm. The other two girls fall in between these two extremes. How could you describe the heights of all four girls with a single number? How could express how they vary in height with another number?
    ::身高各异,身高最短的女孩身高52厘米,身高最高的女孩身高64厘米。 另外两个女孩身高介于这两个极端之间。你如何用一个数字来描述所有四个女孩的身高?如何用另一个数字来说明她们身高的变化?

    Using Statistics to Describe a Sample
    ::使用统计来描述抽样

    The girls in the picture above make up a small sample—there are only four of them. In scientific investigations, samples may include hundreds or even thousands of people or other objects of study. Especially when samples are very large, it’s important to be able to summarize their overall characteristics with a few numbers. That’s where descriptive statistics come in. Descriptive statistics are measures that show the central tendency, or center, of a sample or the variation in a sample.  
    ::以上图中的女孩组成了一个小样本 — — 其中只有四个。 在科学调查中,样本可能包括数百甚至数千人或其他研究对象。 特别是当样本非常庞大时,必须能够用几个数字来总结她们的总体特征。 这就是描述性统计数据的来源。 描述性统计数据是显示样本中心趋势或中心或抽样变化的尺度。

    Describing the Center
    ::描述中心

    The central tendency of a sample can be represented by the mean, median, or mode.
    ::样本的中心趋势可以用平均值、中位数或模式表示。

    • The mean is the average value. It is calculated by adding the individual measurements and dividing the sum by the total number of measurements.
      ::平均值是平均值。计算方法是增加单项测量数,并将总和除以测量总数。
    • The median is the middle value. To find the median, rank all the measurements from smallest to largest and then find the measurement that is in the middle.
      ::中位数是中值。 要找到中位数, 请将所有测量数据从最小排到最大排位, 然后找到中间的测量数据 。
    • The mode is the most common value. It is the value that occurs most often.
      ::模式是最常见的值。 最经常出现的值是该模式。

    Q: A sample of five children have the following heights: 60 cm, 58 cm, 54 cm, 62 cm, and 58 cm. What are the mean, median, and mode of this sample?
    ::问题:5名儿童的抽样有以下高度:60厘米、58厘米、54厘米、62厘米和58厘米。 样本的平均值、中位数和模式是什么?

    A: The mean is (60 cm + 58 cm + 54 cm + 62 cm + 58 cm) ÷ 5 = 58 cm. The median and mode are both 58 cm as well. The mean, median, and mode are not always the same, as they are for this sample. In fact, sometimes these three statistics are very different from one another for the same sample.
    ::A:平均值为(60厘米+58厘米+54厘米+54厘米+62厘米+58厘米) = 5 = 58厘米。中位数和模式均为58厘米。中位数和模式与本样本的平均值、中位数和模式并不总是相同。事实上,对于同一样本,这三种统计数据有时彼此差异很大。

    Describing the Range
    ::描述范围

    Many samples have a lot of variation in measurements. Variation can be described with a statistic called the range . The range is the total spread of values in a sample. It is calculated by subtracting the smallest value from the largest value.
    ::许多样本在测量方面有许多差异。变量可以用一个称为范围的统计数据来描述。范围是样本中数值的总分布。计算方法是从最大值中减去最小值。

    Q: What is the range of heights in the sample of children in the previous question?
    ::问题:上一个问题中儿童抽样中的高度范围是多少?

    A: The range is 62 cm – 54 cm = 8 cm.
    ::A:范围为62厘米 - 54厘米 = 8厘米。

    Summary
    ::摘要

    • Descriptive statistics are measures that summarize the characteristics of a sample.
      ::说明性统计是概括抽样特征的计量尺度。
    • The central tendency, or center, of a sample can be represented by the mean, median, or mode.
      ::样本的中心趋势或中心,可以用平均值、中位数或模式表示。
    • The variation in a sample can be represented by the range, or the total spread of values.
      ::抽样中的差异可以用数值的范围或总分布来表示。

    Review
    ::回顾

    1. What are descriptive statistics, and why are they useful?
      ::什么是描述性统计数字,为什么它们有用?
    2. Find the mean, median, and mode of this set of values: 12 g, 9 g, 13 g, 12 g, 20 g, 17 g, 15 g.
      ::查找这一组数值的平均值、中位数和模式:12g、9g、13g、12g、20g、17g、15g。
    3. What is the range of the set of values in question 2?
      ::问题2中的一组数值的范围是什么?

    Resources
    ::资源