e35aacee-fbe8-4de4-b17a-d80b704d2567 58 4 5 decimal

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

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 :

v i 110 range v i 1 + el i : for v 21 line :

v 0.25 percentile v 0.5 percentile v 0.9 percentile v Median 41 mat 25 9.8 541 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.

Mean

mfg 798546868151 mat :

N mfg length :

1 N / mfg i el i 1 N sum * 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

x μ σ qnorm x μ σ ICDF.Normal :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

y1 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 :

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 Quantiles :

Q 1 0.028 2 0.047 3 0.064 4 0.084 5 0.1 6 0.118 7 0.134 8 0.153 9 0.167 10 0.183 11 0.195 12 0.212 13 0.228 14 0.239 15 0.248 16 0.259 17 0.269 18 0.282 19 0.284 20 0.298 202 mat

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

a X Y Slope : b X Y Intercept : 21 mat 0.014 0.03 21 mat

x f b a x * + :

XY Q o 5 black plot :

Line x 021 0.01 range : i 1 x rows range vy i el x i el f eval : for x vy augment 31 line :

Quantiles over data set

XY Line 2 1 sys

1 time t0 - 3 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 quartiles quartile1 y1 0.25 percentile : quartile2 y1 0.50 percentile : quartile3 y1 0.75 percentile : 31 mat 51.475 56.3 62.05 31 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. That is, the 0.3 (or 30%) quantile is the point at which 30% percent of the data fall below and 70% fall above that value.

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 39.4 000 45.3 000 49.2 000 49.4 000 51.3 000052000 53.2 000 53.2 000 54.9 000 55.5 0000 57.1 000 57.2 000 57.5 000 59.2 000610000 62.4 000 63.8 000 64.3 000 67.3 000 67.7 204 mat

Observe . . . less regular data vector will nicely

split a range search for end purpose wrt % . . . =>

percentile(v,p) sorts the data vector.

Truth table is implicitly sorted .

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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 1 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