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(n+1)/2. If you have an even number, n, of elements, the median is the
average of the elements located in positions n/2 and (n+1)/2. Although the
pre-programmed statistical features of the calculator do not include the
calculation of the median, it is very easily to write a program to calculate such
quantity by working with lists. For example, if you want to use the data in
Σ
DAT to find the median, type the following program in RPN mode (see
Chapter 21 for more information on programming in User RPL language).:
«
nC
«
RCL
Σ
DUP SIZE 2 GET IF 1 > THEN nC COL
−
SWAP DROP
OBJ
1 +
ARRY END OBJ
OBJ
DROP DROP DUP
n
«
LIST SORT
IF ‘n MOD 2 == 0’ THEN DUP ‘n/2’ EVAL GET SWAP ‘(n+1)/2’ EVAL GET +
2 / ELSE ‘(n+1)/2’ EVAL GET END “Median”
TAG
»
»
»
Store this program under the name MED. An example of application of this
program is shown next.
Example 2 – To run the program, first you need to prepare your
Σ
DAT matrix.
Then, enter the number of the column in
Σ
DAT whose median you want to find,
and press
@@MED@@
. For the data currently in
Σ
DAT (entered in an earlier
example), use program MED to show that
Median: 2.15
.
The mode of a sample is better determined from histograms, therefore, we
leave its definition for a later section.
Measures of spread
The variance (Var) of the sample is defined as
∑
=
−
⋅
−
=
n
i
i
x
x
x
n
s
1
2
2
)
(
1
1
.
The standard deviation (St Dev) of the sample is just the square root of the
variance, i.e., s
x
.
The range of the sample is the difference between the maximum and minimum
values of the sample. Since the calculator, through the pre-programmed
statistical functions provides the maximum and minimum values of the sample,
you can easily calculate the range.
