First Steps

Statistical data usually consists of groups of numbers. Devore and Peck [8, Exercise 2.11] describe an experiment in which 22 consumers reported the number of times they had purchased a product during the previous 48 week period. The results are given as a table:
0 2 5 0 3 1 8 0 3 1 1
9 2 4 0 2 9 3 0 1 9 8
To examine this data in XLISP-STAT we represent it as a list of numbers using the "2D list function:
> (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
(0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
>
Note that the numbers are separated by white space (spaces, tabs or even returns), not commas.

The "2D mean function can be used to compute the average of a list of numbers. We can combine it with the "2D list function to find the average number of purchases for our sample:

> (mean (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
3.227273
>
The median of these numbers can be computed as
> (median (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
2
>

It is of course a nuisance to have to type in the list of 22 numbers every time we want to compute a statistic for the sample. To avoid having to do this I will give this list a name using the "2D def special form 4:

> (def purchases (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
PURCHASES
>
Now the symbol "2D purchases has a value associated with it: Its value is our list of 22 numbers. If you give the symbol "2D purchases to the evaluator then it will find the value of this symbol and return that value:
> purchases
(0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
>
We can now easily compute various numerical descriptive statistics for this data set:
> (mean purchases)
3.227273
> (median purchases)
2
> (standard-deviation purchases)
3.279544
> (interquartile-range purchases)
3.5
>

XLISP-STAT also supports elementwise arithmetic operations on lists of numbers. For example, we can add 1 to each of the purchases:

> (+ 1 purchases)
(1 3 6 1 4 2 9 1 4 2 2 10 3 5 1 3 10 4 1 2 10 9)
>
and after adding 1 we can compute the natural logarithms of the results:
> (log (+ 1 purchases))
(0 1.098612 1.791759 0 1.386294 0.6931472 2.197225 0 1.386294 0.6931472 
0.6931472 2.302585 1.098612 1.609438 0 1.098612 2.302585 1.386294 0 
0.6931472 2.302585 2.197225)
>