From the
Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
Boxplots
The Density of Nitrogen
- A Comparison of Two Samples
Lord Raleigh was one of the earliest scientists to study the density of nitrogen. In his studies, he noticed something peculiar. The density of nitrogen produced from chemical compounds tended to be smaller than the density of nitrogen produced from the air.
However, he was working with fairly small samples, and the question is, was he correct in his conjecture?
Lord Raleigh's measurements which first appeared in Proceedings, Royal Society (London, 55, 1894 pp. 340-344) are produced below. The units are the mass of nitrogen filling a certain flask under specified pressure and temperature.
| Chemical | Atmospheric |
| 2.30143 | 2.31017 |
| 2.29890 | 2.30986 |
| 2.29816 | 2.31010 |
| 2.30182 | 2.31001 |
| 2.29869 | 2.31024 |
| 2.29940 | 2.31010 |
| 2.29849 | 2.31028 |
| 2.29889 | 2.31163 |
| 2.30074 | 2.30956 |
| 2.30054 |
1. Calculate the summary statistics for each set of data.
2. Construct side-by-side box plots.
Note the difference in the IQR for each set of data, as well as the difference in variability. From this we can assume that the two sets of data are not from the same population.
This set of data helped Raleigh conclude that another gas was present in the atmosphere, and lead to the discovery of argon.
The table on this page displays the Test batting averages in the period 1946-49 for all batsmen who averaged over 40.
Display the data using whichever graphical displays you think are most appropriate.
Comment on the distribution.
Is Don Bradman an outlier, over the period 1946-49?
Source: Bradmanesque, a worksheet by Vince Geiger, Hillbrook Anglican School
| Name | Cou | Avge |
| D.G.Bradman | AUS | 105.72 |
| E.de C.Weekes | WI | 82.46 |
| A.D.Nourse | RSA | 68.60 |
| A.R.Morris | AUS | 67.00 |
| S.G.Barnes | AUS | 66.53 |
| D.C.S.Compton | ENG | 61.95 |
| B.Mitchell | RSA | 59.55 |
| A.L.Hassett | AUS | 58.10 |
| A.Melville | RSA | 55.27 |
| W.J.Edrich | ENG | 53.09 |
| L.Hutton | ENG | 51.97 |
| J.D.B.Robertson | ENG | 51.90 |
| R.S.Modi | IND | 49.78 |
| V.S.Hazare | IND | 49.77 |
| E.A.B.Rowan | RSA | 48.10 |
| C.Washbrook | ENG | 47.85 |
| J.Hardstaff jnr. | ENG | 47.16 |
| D.G.Phadkar | IND | 46.16 |
| C.L.Walcott | WI | 45.00 |
* a batting average is calculated by dividing the total number of runs scored by a player by the number of times they've been dismissed.
Twenty-six samples of Romano-British pottery were found at four different kiln sites in Wales, Gwent and the New Forest. The sites are Llanederyn (L), Caldicot (C), Island Thorns (I), and Ashley Rails (A). The other variables are the percentage of oxides of various metals measured by atomic absorption spectrophotometry. The data were collected to see if different sites contained pottery of different chemical compositions.
a. Using the boxplots, describe some of the notable features of these data.
b. Which areas are most similar to each other in terms of the composition of the pottery? Give evidence for your statement.
c. There appears to be less spread in the data from Caldicot. Can you give an explanation as to why this might be?
Source: Data and Story Library; from Tubb, A., Parker, A.J. and Nickless, G. (1980), The analysis of Romano-British pottery by atomic absorption spectrophotometry. Archaeometry, 22, 153-171.
Variable Description
1. Al: Percentage of aluminum oxide in sample
2. Fe: Percentage of iron oxide in sample
3. Mg: Percentage of magnesium oxide in sample
4. Ca: Percentage of calcium oxide in sample
5. Na: Percentage of sodium oxide in sample
6. Site: Site where pottery sample was collected
The Data
Al |
Fe |
Mg |
Ca |
Na |
Site |
14.4 |
7.00 |
4.30 |
0.15 |
0.51 |
L |
13.8 |
7.08 |
3.43 |
0.12 |
0.17 |
L |
14.6 |
7.09 |
3.88 |
0.13 |
0.20 |
L |
11.5 |
6.37 |
5.64 |
0.16 |
0.14 |
L |
13.8 |
7.06 |
5.34 |
0.20 |
0.20 |
L |
10.9 |
6.26 |
3.47 |
0.17 |
0.22 |
L |
10.1 |
4.26 |
4.26 |
0.20 |
0.18 |
L |
11.6 |
5.78 |
5.91 |
0.18 |
0.16 |
L |
11.1 |
5.49 |
4.52 |
0.29 |
0.30 |
L |
13.4 |
6.92 |
7.23 |
0.28 |
0.20 |
L |
12.4 |
6.13 |
5.69 |
0.22 |
0.54 |
L |
13.1 |
6.64 |
5.51 |
0.31 |
0.24 |
L |
12.7 |
6.69 |
4.45 |
0.20 |
0.22 |
L |
12.5 |
6.44 |
3.94 |
0.22 |
0.23 |
L |
11.8 |
5.44 |
3.94 |
0.30 |
0.04 |
C |
11.6 |
5.39 |
3.77 |
0.29 |
0.06 |
C |
18.3 |
1.28 |
0.67 |
0.03 |
0.03 |
I |
15.8 |
2.39 |
0.63 |
0.01 |
0.04 |
I |
18.0 |
1.50 |
0.67 |
0.01 |
0.06 |
I |
18.0 |
1.88 |
0.68 |
0.01 |
0.04 |
I |
20.8 |
1.51 |
0.72 |
0.07 |
0.10 |
I |
17.7 |
1.12 |
0.56 |
0.06 |
0.06 |
A |
18.3 |
1.14 |
0.67 |
0.06 |
0.05 |
A |
16.7 |
0.92 |
0.53 |
0.01 |
0.05 |
A |
14.8 |
2.74 |
0.67 |
0.03 |
0.05 |
A |
19.1 |
1.64 |
0.60 |
0.10 |
0.03 |
A |
The Boxplots
