【统计学】第三章

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数据的预处理包括哪些内容？

1.数据审核
2.数据筛选
3.数据排序
4.数据透视表

分类数据和顺序数据的整理和图示方法各有哪些？

1.分类数据整理：对于定性数据，使用频数分布进行描述，还可以进行比例、百分比、比率等级统计量描述。

• 分类数据的图示
• 条形图
• 帕累托图
• 饼图
• 环形图

2.顺序数据整理： 对于顺序数据，除了可以使用以上整理和显示技术，还可以计算累积频数和累积频率(百分比)

• 顺序数据的图示
• 折线图

数值型数据的分组方法有哪些？简述组距分组的步骤。

数据分组的主要目的是观察数据的分布特征。数据经分组后再计算出各组中数据出现的频数，就形成了一张频数分布表。
数据分组的方法有单变量值分组和组距分组两种。

• 确定组数
• 确定各组的组距
• 根据分组整理成频数分布表

直方图与条形图有何区别？

首先，条形图是用条形的长度表示各类别频数的多少，其宽度(表示类别)则是固定的；直方图是用面积表示各组频数的多少。矩形的高度表示每一组的频数或频率，宽度则表示各组的组距，因此其高度与宽度均有意义。
其次，由于分组数据具有连续性，直方图的各矩形通常是连续排列，而条形图则是分开排列。
条形图用于展示分类数据，而直方图用于展示数值型数据

绘制线图应注意哪些问题？

绘制线图时，时间一般绘在横轴，观测值在纵轴。一般应该绘成横轴略大于纵轴的长方形，其长宽比例大致为10:7.
图形过扁或过于瘦高，不仅不美观，而且会给人造成视觉上的错觉，不便于对数据变化的理解。一般情况下，纵轴数据下端应从"0"开始，以便于对数据变化的理解。一般情况下，纵轴数据下端应从"0"时开始，便于比较。如果数据"0"之间的间距过大，可以采取折断的符号将纵轴折断。

饼图和环形图有什么不同？

饼图与环形图类似，但是又有区别。环形图中间有一个"空洞"，每个样本用一个环来表示，样本中的每一部分数据用环中的一段表示。因此环形图可显示多个样本各部分所占的响应比例，从而有利于对构成的比较研究。

茎叶图和环形图相比有什么优点？它们的应用场合是什么？

茎叶图是反映原始数据分布的图形。它由茎和叶两部分构成，其图形是由数字组成的。通过茎叶图，可以看出数据的分布形状及数据的离散程度，比如是否对称，数据是否集中，是否有离群点，等等。
茎叶图类似于横置的直方图，与直方图对比，茎叶图既能给出数据的分布状况，又能给出每一个原始数值，即保留了原始数据的信息。而直方图虽然能很好的显示数据的分布，但是不能保留原始的数值。在应用方面，直方图通常适用于大批量数据，茎叶图通常适用于小批量数据。
环形图可显示多个样本各部分所占的相应比例，从而有利于对构成的比较研究。

鉴别图表优劣的准则有哪些？

• 1.一张好图应当静心设计，有助于洞察问题的实质。
• 2.一张好图应当使复杂的观点得到简明、确切、高效的阐述。
• 3.一张好图应当能在最短的时间内以最少的笔墨给读者提供大量的信息。
• 4.一张好图应当是多维的。
• 5.一张好图应当表述数据的真实情况。
  在绘制图形时，应避免一切不必要的修饰。过于花哨的修饰往往会使人注重图形本身，而掩盖了图形所要表达的信息。图形产生的视觉效果应与数据所体现的事物特征相一致，否则有可能歪曲数据，给人留下错误的印象。

制作统计表应注意哪些问题？

• 首先，要合理安排统计表的结构，比如行标题、列标题、数据资料的位置应安排合理。当然，由于强调的问题不同，行标题和列标题可以互换，但是应使统计表的横竖长度比例适当，避免出现过高或过宽的表格形式。
• 其次，表头一般应包括表号、总标题和表中的数据的单位等内容。总标题应简明确切地概括出统计表的内容，一般需要说明统计数据的时间，地点以及何种数据，即标题内容应满足3W要求。如果表中的全部数据都是同一个计量单位，可在表的右上角标明。若各变量的计量单位不同，则应放在每个变量后或单列出一列标明。
• 再次，表中的上下两条横线一般用粗线，中间的其他线要用细线，这样使人看起来清除、醒目。通常情况下，统计表的左右两边不封口，列标题之间在必要时可用竖线分开，而行标题之间通常不必用横线隔开。总之表中尽量少用横竖线。表中的数据一般是右对齐，有小数点时应以小数点对齐，而且小数点的位数应统一。对于没有数据的表格单元，一般用"-"表示，一张填好的统计表不应出现空白单元格。

错题集

• 1.样本或总体中各不同类别数值之间的比值称为比率
• 2.将比例乘以100得到的数值称为百分数
• 3.饼图最适合描述结构性问题
• 4.环形图适合于比较研究两个或多个样本或总体的结构性问题
• 5.最适合描述一组数据分布的图形是直方图
• 6.对于大批量的数据，最适合描述分布的图形是直方图
• 7.对于小批量的数据，最适合描述分布的图形是茎叶图
• 8.对于时间序列数据，用于描述其变化趋势的图形通常是箱线图
• 9.气泡图主要用于描述三个变量之间的相关关系
• 10.与直方图相比茎叶图保留了原始数据的信息
• 11.茎叶图不适合描述分类数据
• 12.直方图与条形图的区别之一是直方图的各矩形通常是连续排列的，而条形图则是分开排列的

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