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In Exploratory Data Analysis, Tukey (1977) demonstrates the box‐and‐whiskers plot using the Lord Rayleigh data, which measure the weight of nitrogen gas obtained by various means; see Table 1.1. Discrepancies in the results led to his discovery of the element argon. Rayleigh made measurements from 1892 to 1894, with a mean of 2.30584 and a standard deviation of 0.00537. It is common to assume such measurements of a fundamental quantity are normally distributed. Multiple experiments are run and the results averaged in the presumption that a more accurate estimate will result.

Table 1.1 Lord Rayleigh's 24 measurements (sorted) of the weight of a sample of nitrogen. The first 10 came from chemical samples, while the last 14 came from pure air.

2.29816	2.29849	2.29869	2.29889	2.29890
2.29940	2.30054	2.30074	2.30143	2.30182
2.30956	2.30986	2.31001	2.31010	2.31010
2.31012	2.31017	2.31024	2.31024	2.31026
2.31027	2.31028	2.31035	2.31163

Figure 1.3 Displays of Lord Rayleigh's 24 measurements of the atomic weight of nitrogen gas. (Left) Histogram with four bins; (middle) a second histogram; (right) stem‐and‐leaf display using the command .

In the left frame of Figure 1.3, we display a histogram with four (carefully selected) bins. The histogram is shown on a density scale, rather than a frequency scale, so that the area of the shaded region is 1. We shall see in Problem 1 that this is accomplished by dividing the bin counts by .

The first histogram in Figure 1.3 hides the interesting structure contained in the small dataset. The second histogram and stem‐and‐leaf plot show the two clusters quite clearly. Charting of data before the 1900s was not common, and looking at a table of the data would typically not reveal this feature. It turned out that Lord Rayleigh had combined various sources of the gas with several purifying agents and extraction methods. The samples originating from “pure air” were “contaminated” with argon. For the discovery of argon, Lord Rayleigh was awarded the Nobel Prize in Physics in 1904.