Tabulation and the data matrix

Small samples of data are best presented in the form of a table ^2.1. For example, Table 2.1 below presents the age, height, and weight of a sample of some colleagues at the Department of Meteorology in the University of Reading. There are $n=11$ objects (or individuals or units) in the sample with $p=3$ observed variables age, height, and weight. Note that for good clarity and typesetting, published tables should not include ANY vertical lines or shading even if certain word processors allow such features.

Table: Some bodily characteristics of a small sample of (unnamed !) meteorologists in the Department of Meteorology at the University of Reading.

Person	Age (years)	Height (cm)	Weight (kgs)
1	30.9	180	76
2	26.9	164	64
3	33.2	176	87
4	28.5	172	75
5	32.3	176	75
6	37.0	180	86
7	38.3	171	65
8	31.5	172	76
9	32.8	161	75
10	37.7	175	85
11	29.1	190	83

The table of numbers can be considered to be a rectangular data matrix ${\bf X}$ having $n=11$ rows and $p=3$ columns. The data matrix ${\bf X}$ has dimension $(n\times p)$ and elements $x_{ij}$ where the first subscript $i=1$, 2, ..., $n$ is the object index and the second subscript $j=1$, 2, ..., $p$ is the variable index. Note: it is conventional to denote variables by columns and sample objects by rows.

The rest of this lecture will focus on the special case of descriptive methods for univariate data $\{x_i : i=1, 2, \ldots, n\}$ having only one variable ($p=1$). Many descriptive methods have also been developed for exploring multivariate data having more than one ($p>1$) variable and some of these will be covered in later lectures.