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统计代写|数据可视化代写Data visualization代考|Johann Lambert

Between 1760 and 1777, Johann Heinrich Lambert [1728-1777] described curve fitting and interpolation from empirical data. Lambert, a Swiss polymath who made many contributions to mathematics, astronomy, color theory, and experimental sciences, was one of the first scientists to use graphs to represent experimental data, with an aim to show how algebraic methods could be applied to hand-drawn curves representing empirical observations. ${ }^4 \mathrm{He}$ was a seeker of the mathematical laws governing physical phenomena.

Figure $6.4$ shows a chart of soil temperatures in degrees Fahrenheit at a range of latitudes (individual curves) at some intervals of time over the year. The curves were derived from observational data, but no data points are shown. It is a fine example of an early graph, and it very clearly shows the phenomenon he sought to depict-very little variation at the equator and much greater variation toward the poles.

Yet a closer reading of Lambert’s works shows that he had the essential ideas of the scatterplot and should be considered one of the founding fathers of data visualization, particularly for scientific phenomena. In a variety of works on topics of mortality, physics (color, light, hygrometry), and astronomy from 1760 to 1780 , he consistently used graphs of data in an attempt to develop theory from fallible observations in such a way as to deal with a theory of errors. In several works he describes his use of graphs in a way that could be considered modern. One particularly clear statement appeared in 1765 :
We have in general two variable quantities $x, y$, which will be collated with one another by observation, so that we can determine for each value of $x$, which may be considered as an abscissa, the corresponding ordinate $y$. Were the experiments or observations completely accurate these ordinates would give a number of points through which a straight or curved line should be drawn. But as thus is not so, the line deviates to a greater or lesser extent from the observational points. It must therefore be drawn in such a way that it comes as near as possible to its true position and goes, as it were, through the middle of the given points. 5

统计代写|数据可视化代写Data visualization代考|Why Not Playfair

Thus, well before 1800 , all the necessary intellectual pieces for the graphing of empirical data on abstract $2 \mathrm{D}$ coordinate systems were in place. So, when Playfair devised nearly all of the common statistical graphs-first the line graph and bar chart in the Commercial and Political Atlas, later the pie chart and circle graph in the Statistical Breviary-one might wonder why he did not develop the scatterplot for data, the idea of plotting one variable against another.

Playfair was primarily concerned with economic data recorded over time, often for comparative purposes, so the time-series line graph seemed an ideal format. Indeed, all but one of the forty-four charts in the first edition of the Commercial and Political Atlas were line graphs, often showing two time series (imports and exports), so he could discuss the balance of trade as the difference between the curves.

The idea of plotting imports against exports apparently did not occur to him and probably would not have aided his arguments. In 1821 in a brief pamphlet, Letter on Our Agricultural Distresses, Playfair attempted something far more ambitious: to try to show the relationship between different time series and how these fit in terms of historical events. Plate 10 shows three parallel time series over a 250-year period, reflecting prices (price of a quarter of wheat in shillings), wages for labor (weekly wage for a good mechanic, in shillings), and the ruling British monarch.

Playfair shows the time series for wages as a line graph; its vertical scale on the left has a range of $0-100$, but the data (wages) range only from 0 to 30 . The time series for prices of wheat is shown as a bar graph using the right vertical scale, also with a range of $0-100$.

Both vertical axes are in shillings, but the perception of their relative trends would change dramatically if the scales were changed from weekly to daily or monthly wages or if prices of wheat were changed to units of a loaf or a full bushel. But mixing different scales ( $y$-axes), here wages and wheat prices, on the same plot is considered sinful today because it allows a sinning plotter to independently manipulate the two scales and make the relation between those two variables take anv form thev like.

统计代写|数据可视化代写Data visualization代考|INFO2001

统计代写|数据可视化代写Data visualization代考|Johann Lambert

在 1760 年至 1777 年间,约翰·海因里希·兰伯特 [1728-1777] 描述了根据经验数据进行曲线拟合和插值。兰伯特是一位瑞士博学家,对数学、天文学、色彩理论和实验科学做出了许多贡献,他是最早使用图表来表示实验数据的科学家之一,旨在展示代数方法如何应用于手绘代表经验观察的曲线。4H和是支配物理现象的数学规律的探索者。

数字6.4显示了一年中某些时间间隔在一定纬度范围内以华氏度为单位的土壤温度图表(单条曲线)。曲线来自观察数据,但没有显示数据点。这是早期图表的一个很好的例子,它非常清楚地显示了他试图描绘的现象——赤道的变化非常小,而两极的变化则大得多。

然而,仔细阅读兰伯特的作品可以看出,他拥有散点图的基本思想,应该被认为是数据可视化的创始人之一,尤其是对于科学现象。在 1760 年至 1780 年间有关死亡率、物理学(颜色、光线、湿度测量)和天文学的各种著作中,他始终使用数据图表,试图从错误的观察中发展出理论,从而处理错误理论。在几部作品中,他以一种可以被认为是现代的方式描述了他对图表的使用。1765 年出现了一个特别明确的陈述:
我们通常有两个变量X,是,将通过观察相互比较,以便我们可以确定每个值X,可以认为是横坐标,对应的纵坐标是. 如果实验或观察完全准确,这些纵坐标将给出一些点,应通过这些点绘制直线或曲线。但事实并非如此,这条线或多或少地偏离了观测点。因此,它必须以尽可能接近其真实位置的方式绘制,并且可以说是通过给定点的中间。5

统计代写|数据可视化代写Data visualization代考|Why Not Playfair

因此,早在 1800 年之前,所有必要的知识部分都可以在摘要上绘制经验数据的图表。2D坐标系已经到位。因此,当 Playfair 设计了几乎所有常见的统计图表时——首先是商业和政治地图集中的折线图和条形图,后来是统计书卷中的饼图和圆形图——人们可能会想知道为什么他没有开发散点图数据,将一个变量与另一个变量作图的想法。

Playfair 主要关注随时间记录的经济数据,通常是出于比较目的,因此时间序列折线图似乎是一种理想的格式。事实上,在第一版《商业和政治地图集》的 44 张图表中,除了一个以外,所有图表都是折线图,通常显示两个时间序列(进口和出口),因此他可以将贸易平衡讨论为曲线之间的差异.

他显然没有想到将进口与出口相提并论,也可能不会帮助他的论点。1821 年,普莱费尔在一本简短的小册子《关于我们的农业困境的信》中尝试了更为雄心勃勃的事情:试图展示不同时间序列之间的关系以及它们如何适应历史事件。图 10 显示了 250 年期间的三个平行时间序列,反映了价格(以先令计算的四分之一小麦的价格)、劳动力工资(以先令计算的优秀技工的周工资)和执政的英国君主。

Playfair 将工资的时间序列显示为折线图;它在左侧的垂直刻度范围为0−100,但数据(工资)范围仅从 0 到 30 。小麦价格的时间序列显示为使用右侧垂直刻度的条形图,范围也为0−100.

两个垂直轴都以先令为单位,但如果将比例从每周工资改为每天或每月工资,或者如果小麦价格改为面包或整蒲式耳的单位,则对它们相对趋势的看法将发生巨大变化。但是混合不同的尺度(是-axes),这里的工资和小麦价格,在今天被认为是有罪的,因为它允许有罪的绘图员独立地操纵这两个尺度,并使这两个变量之间的关系采取类似的形式。

统计代写|数据可视化代写Data visualization代考

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