Example $1\mathrm{.}1($A data array$)$ A selection of four receipts from a university bookstore

was obtained in order to investigate the nature of book sales. Each receipt provided,

among other things, the number of books sold and the total amount of each sale. Let

the first variable be total dollar sales and the second variable be number of books

sold. Then we can re&ard the corresponding numbers on the receipts as four measurements on two variables. Suppose the data, in tabular form, are

Variable $1($dollar sales$)$: $42524858$

Variable $2($number of books$)$: $4543$

Using the notation just introduced, we have

Xll $=42$ X$2$l $=52$ X$3$l $=48$ X$4$l $=58$

X$12=4$ X$22=5$ X$32=4$ X$42=3$

and the data array X is

l

$424$l X $=525$

$484$

$583$

with four rows and two columns. $$

Considering data in the form of arrays facilitates the exposition of the subject

matter and allows numerical calculations to be performed in an orderly and efficient

manner. The efficiency is twofold, as gains are attained in both $(1)$ describing numerical calculations as operations on arrays and $(2)$ the implementation of the calculations on computers, which now use many languages and statistical packages to

perform array operations. We consider the manipulation of arrays of numbers in

Chapter $2.$ At this point, we are concerned only with their value as devices for displaying data.