<p> Percentiles </p>

e35aacee-fbe8-4de4-b17a-d80b704d2567 107 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Quantiles ...

v p percentile n v rows : pos1 p n * p + (0 - : position 0 pos1 0 ≤ pos1 0 pos1 < (n 1 - < n 1 - pos1 n 1 - ≥ cases : between position position Floor - : sorted v sort : percentile sorted position Floor el between sorted position Ceil el sorted position Floor el - (* + : percentile 71 line eval :

v i 117 range v i 1 + el i : for v 21 line :

v 0.45 percentile v 0.5 percentile v 0.55 percentile v Median 41 mat 7.55 8.5 9.45 8.5 41 mat

t0 1 time :

MODE: of a data set is the value that occurs with greatest frquency. MEDIAN: or "middle value" of a data set is another metric for central location. It is less sensitive to "outliers" or small changes in data. A median is the value falling in the middle when data are sorted in ascending order. If there are an odd number of data, there will be one data value which is the median.

mfg 798546868151 mat :

Mean

N mfg length :

1 N / mfg i el i 1 N sum * 75.4

mfg Mean 75.4

quartile1 mfg 0.25 percentile : quartile2 mfg 0.5 percentile : quartile3 mfg 0.75 percentile : 31 mat 62.5 81 85.5 31 mat

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

y1 vector is borrowed from a random histogram

y1 558101218241420161516121214392181 mat :

v Quantiles j 1 v rows range p j el 100 j * v j el / 0.3175 + 100 0.365 + / : x j el j : 21 line for x p augment 21 line :

Q y1 sort Quantiles :

Q 1 0.501 2 0.667 3 0.601 4 0.8 5 0.626 6 0.667 7 0.701 8 0.667 9 0.75 10 0.833 11 0.786 12 0.857 13 0.867 14 0.875 15 0.937 16 0.889 17 0.85 18 0.75 182 mat

39.4 45.3 49.2 49.4 51.3 52 53.2 53.2 54.9 55.5 57.1 57.2 57.5 59.2 61 62.4 63.8 64.3 67.3 67.7 201 mat

X Q 1 col : Y Q 2 col : 21 line

a X Y Slope : b X Y Intercept : 21 mat 0.018 0.59 21 mat

x f b a x * + :

XY Q o 5 black plot :

Quantiles over data set

XY x f 2 1 sys

1 time t0 - 0.6 s *

In statistics and the theory of probability, quantiles are cutpoints dividing the range of a probability distribution into contiguous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one less quantile than the number of groups created.

The 3 contiguous quantiles quantile1 y1 0.4 percentile : quantile2 y1 0.50 percentile : quantile3 y1 0.6 percentile : 31 mat 11.2 121431 mat

A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set. By a quantile, we mean the fraction (or percent) of points below the given value. i.e: the 0.3 (or 30%) quantile is the point at which 30% percent of the data fall below and 70% fall above that value.

Quantiles ... around mean

y1 0.153 0.264 0.3 0.326 0.335 0.476 0.493 0.961 0.964 1.088 1.123 1.236 1.274 1.28 1.304 1.402 1.946 2.007 2.03 3.645 201 mat :

The 3 contiguous quantiles quantile1 y1 0.45 percentile : quantile2 y1 0.50 percentile : quantile3 y1 0.55 percentile : 31 mat 1.0198 1.1055 1.1852 31 mat

s 1 :

X s y1 * : x c1 X 1 el x ≤ (x quantile1 ≤ (* : x c2 quantile1 x ≤ (x quantile2 ≤ (* : x c3 quantile2 x ≤ (x quantile3 ≤ (* : x c4 quantile3 x ≤ (x X X rows el ≤ (* : split X c1 X * vectorize X c2 X * vectorize X c3 X * vectorize X c4 X * vectorize augment : 61 sys

split 0.153 000 0.264 000 0.3 000 0.326 000 0.335 000 0.476 000 0.493 000 0.961 000 0.964 0000 1.088 0000 1.123 0000 1.236 000 1.274 000 1.28 000 1.304 000 1.402 000 1.946 000 2.007 000 2.03 000 3.645 204 mat

data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

Mode("1:matrix", "2:variable") - Returns the mode value from a sample and the number of occourrences.

y 558101218241420161516121214392181 mat :

y Mean y Median 21 sys 11.9444 1221 sys

native NOT convenient y_Mode 1211 mat 311 mat 21 mat

mode 12
3 times y Mode UnestV 12321 mat

U 19 Random :

percentiles around median ...
percentiles are in 'values'
... or  in units '%'
percentile(U,0.5) = median. U 0.49 percentile U 0.5 percentile U 0.51 percentile U Median 41 mat 0.4674 0.483 0.4854 0.483 41 mat

x 0 0.5 pdf.Normal x 0 0.25 pdf.Normal 2 1 sys

x Δσ x 0 0.5 pdf.Normal x 0 0.25 pdf.Normal - :

x Δσ x 0.5 - 0.5 solve 0.3399 - 0.3399 21 mat

jmG: 20230108

Quartiles ... around mean

y1 0.153 0.264 0.3 0.326 0.335 0.476 0.493 0.961 0.964 1.088 1.123 1.236 1.274 1.28 1.304 1.402 1.946 2.007 2.03 3.645 201 mat :

The 3 contiguous quartiles quartile1 y1 0.25 percentile : quartile2 y1 0.50 percentile : quartile3 y1 0.75 percentile : 31 mat 0.3703 1.1055 1.3775 31 mat

X y1 : x c1 X 1 el x ≤ (x quartile1 ≤ (* : x c2 quartile1 x ≤ (x quartile2 ≤ (* : x c3 quartile2 x ≤ (x quartile3 ≤ (* : x c4 quartile3 x ≤ (x X X rows el ≤ (* : split X c1 X * vectorize X c2 X * vectorize X c3 X * vectorize X c4 X * vectorize augment : 61 sys

split 0.153 000 0.264 000 0.3 000 0.326 000 0.335 0000 0.476 000 0.493 000 0.961 000 0.964 000 1.088 0000 1.123 000 1.236 000 1.274 000 1.28 000 1.304 0000 1.402 000 1.946 000 2.007 000 2.03 000 3.645 204 mat

jmG: 20230108

Percentiles sub-utility ... split 'v' over 'n'

<p> Percentiles </p>

v p percentile n v rows : pos1 p n * p + (0 - : position 0 pos1 0 ≤ pos1 0 pos1 < (n 1 - < n 1 - pos1 n 1 - ≥ cases : between position position Floor - : sorted v sort : percentile sorted position Floor el between sorted position Ceil el sorted position Floor el - (* + : percentile 71 line :

t 20 :

v i 1 t range v i 1 + el i t / : for v 21 line :

v 0.45 percentile v 0.5 percentile v 0.55 percentile v Median 41 mat 0.445 0.5 0.555 0.5 41 mat

n 0.1 0.9 0.125 range :

my% n v n percentile vectorize augment :

my% 11 mat 0.1 0.06 0.125 0.088 0.15 0.115 0.175 0.142 0.2 0.17 0.225 0.198 0.25 0.225 0.275 0.252 0.3 0.28 0.325 0.308 0.35 0.335 0.375 0.362 0.4 0.39 0.425 0.418 0.45 0.445 0.475 0.472 0.5 0.5 0.525 0.528 0.55 0.555 0.575 0.582 0.6 0.61 0.625 0.638 0.65 0.665 0.675 0.692 0.7 0.72 0.725 0.748 0.75 0.775 0.775 0.802 0.8 0.83 0.825 0.858 0.85 0.885 0.875 0.912 0.9 0.94 332 mat 11 mat

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data 1 t 1 + (range (t 2 + / v augment (:

data data . 14 black plot :

P my% . 10 red plot :

P data 2 1 sys

V sub subspace j 1 V rows 1 - (range Vsub j el i 1 sub range vx i el V j el i sub / V 1 j + el V j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for V 1 el v stack 31 line 21 line :

N v 4 subspace :

N 0 0.0125 0.025 0.0375 0.05 0.0625 0.075 71 mat

N rows 81

v rows 21