# Calculation Of Percentiles - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

To access the summary stats... option, use: ‚Ù˜˜˜@@@OK@@@
Select the column numbers corresponding to the x- and y-data, i.e., X-Col:
1, and Y-Col: 2.
Using the @ CHK@ key select all the options for outputs, i.e., _ΣX, _ΣY, etc.
Press @@@OK@@@ to obtain the following results:
ΣX: 24.2, ΣY: 11.72, ΣX2: 148.54, ΣY2: 26.6246, ΣXY: 12.602, NΣ:8
Note: There are two other applications under the STAT menu, namely,
and
Hypth. tests..
6. Conf. Interval..
later in the chapter.

## Calculation of percentiles

Percentiles are measures that divide a data set into 100 parts. The basic
procedure to calculate the 100⋅p-th Percentile (0 < p < 1) in a sample of size
n is as follows:
1. Order the n observations from smallest to largest.
2. Determine the product n⋅p
A. If n⋅p is not an integer, round it up to the next integer and find the
corresponding ordered value.
B. If n⋅p is an integer, say k, calculate the mean of the k-th and (k-1) th
ordered observations.
Note: Integer rounding rule, for a non-integer x.yz..., if y ≥ 5, round up to
x+1; if y < 5, round up to x.
This algorithm can be implemented in the following program typed in RPN
mode (See Chapter 21 for programming information):
« SORT DUP SIZE
p X n « n p *
k GET X k 1 + GET + 2 / ELSE k 0 RND X SWAP GET END " " "
These two applications will be discussed
k « IF k CEIL k FLOOR - NOT THEN X
5.
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