N

b1fc361d-63fc-4ce6-b121-b3672be3e0db 25 4 5 decimal

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

N

N 15214334555667138109610911151213137147151016617218121913201021122252312241125112617277282299305313329331634113513367379389397409417428431344114544611479486497501851115255313548551256165785813591660561862763664765116646796856917708711372137313741275137617747887914808811182118312841285486487188689159011911092293129413958961597139889910100141011210271036104121051510681074108111091211031111311281131311416115101161111712118101198120161215122161236124161251112614127212891290130113141327133713491351213681371113891391014017141414213143414417145121461614712148101491415031514152121532154315511156815715158111591016091618162916310164116551661716717168316911170111711017281734174121751717681771217811179101801218110182131831118491850186161872188318911190319117192121935194919511196919761983199720052002 mat :

Utilities

M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Stem plot for QuickPlot unicolor data Stem stem 0 : stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - (range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - (range V V stem j el stack : for V V data data rows row stack : 81 line :

size min max vx Hist Paul W. MCD 11 => Smath vx last vx rows : numbins max min - size / : hist numbins el 0 : i 1 numbins range bin_mid i el i 1 + (size * size 2 / - : j 1 vx last range i size * vx j el ≤ (i 1 + (size * < hist i el hist i el 1 + : N/A if for 21 line for bin_mid hist vx last / augment 61 line :

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 :

Part 0: Histogram normal integer data set

μ N 2 col Mean : 9.29

N rows 200

'N' is randomNormal generated, histogram is therefore PDFnormal. Cumulative weighted classification can be used to identify the PDF that best fit the data set. Is our data set PDFnormal ?.. YES.

rn N 0 μ Scale :

bin 20 : size 1 bin / : min 0 : max 1 : 41 line

vy rn 2 col : H size min max vy Hist : 21 line

μ vy Mean : σ vy StdDev : 21 mat 0.4315 0.1956 21 mat

σ μ sqrt 2 / : 0.328

Cumulative weighted clssification

H Stem x 2 μ * σ pdf.Normal 1 * 0.825 * 2 μ * 1.5 2 μ * 0.5 - 2 2 mat 3 1 sys

Normal random from source creator

N Stem 0 2 1 sys

Part 1: Histogram integer data set

N N 2 col sort :

counts specific values in a sorted vector value table count k 1 : j k table rows range table j el value ≡ index k el j : k k 1 + : 21 line No match if for index rows 31 line :

collect all the counted values in sorted 'N' N bin histogram bin N max ≤ i 0 bin range x i 1 + el i : count i 1 + el i N count : 21 line for x count augment 21 line over bin if 11 line :

H N 18 histogram :

bin N max ≤

Brute force alternative: for small values data set scale and round integers.

low N min : upp N max : 21 mat 01821 mat

μ N Mean : σ N StdDev : 21 mat 9.29 4.21 21 mat

n N length : h upp low - H rows / : 21 mat 200 0.9474 21 mat

To best Engineer collected data: 1. Measuring equipment should be ~ 10 times more accurate than the measured. 2. Make sure the collected data haven't been freaked by else, i.e: raw from collection. Data set not raw from source => recycle.

Stem & bar plots stem H Stem : bar H 0.1 BarSize : 21 line

s 0.25 :

vx 0 n 1 range :

Sigma μ σ - s - μ σ - s μ σ + s μ σ + s - μ σ - s - 52 mat :

vy vx μ σ pdf.Normal n * h * vectorize :

xy vx vy augment :

xy xy . 11 black plot :

Stem style histogram fitted PDFnormal... μ, σ

x μ σ pdf.Normal n * h * stem μ 40 μ 10 - 2 2 mat xy Sigma 6 1 sys bar x μ σ pdf.Normal n * h * μ 40 μ 10 - 2 2 mat 3 1 sys

μ σ ±

Part 2: Simulate/collect/expose 100 measured values

borrowed from Russia. N μ σ rnorm N Random μ σ ICDF.Normal 2 col 11 line :

σ 13 / :

μ 50 :

N 100 :

n 100 :

j 1 N range v j el j μ σ rnorm eval : for

v v n el eval :

Vy v 1 round vectorize :

N Vy sort :

data Strip stripped repeated in 'data' u data 1 col : k 0 : i 1 data rows 1 - (range u i 1 + el u i el ≤ (u i 1 + el u i el ≥ (¤ R k k 1 + : el u i el : 11 line Undefined if 11 line for 21 line v R 1 el : j 2 R rows range v v R j el stack : for v 61 line :

Spool to file Strip N Strip :

CWD C:\SmathFile CurrentDirectory :

Strip CWD HistoDemo wfile 1

Strip CWD HistoDemo rfile :

counts specific values in a sorted vector value table count k 1 : j k table rows range table j el value ≡ index k el j : k k 1 + : 21 line No match if for index rows 31 line :

μ Strip Mean : σ Strip StdDev : 21 mat 50.044 0.487 21 mat

j 1 Strip rows range Hist j el Strip j el N count : for h Strip Hist augment : 21 line

user scale plot α 10 :

h Stem x μ σ pdf.Normal α * 2 1 sys Γ(x) [15 D] Alvaro Same otherwise

Γ 0.99999999999999709182 57.156235665862923517 59.597960355475491248 - 14.136097974741747174 0.49191381609762019978 - 0.33994649984811888699 104 -^* 0.46523628927048575665 104 -^* 0.98374475304879564677 104 -^* - 0.15808870322491248884 103 -^* 0.21026444172410488319 103 -^* - 0.21743961811521264320 103 -^* 0.16431810653676389022 103 -^* - 0.84418223983852743293 104 -^* 0.26190838401581408670 104 -^* - 0.36899182659531622704 105 -^* 151 mat :

ζ Γ z ζ 1 - : zh z 0.5 + : zg zh 607128 / + : zp zg 0.5 zh *^: 14 mat 2 π * sqrt Γ 1 el Γ κ 1 + el z κ + / κ 114 sum + (* zp 2^* zg - exp * eval 21 line :

Valid for Re(ζ)>0

Ucertainty on vector of target values

v# incertitude n v# length : u v# StdDev n sqrt / n 1 - 2 / Γ n 1 - sqrt * n 2 / Γ 2 sqrt * / * : 21 line :

v Mean 50.02

MCD 0.00418 v incertitude 0.03

U v incertitude ± : 0.03 0.03 - 21 sys

v Mean U + 50.05 49.99 21 sys

4 decimals x Γ x Gamma ≡

v Mean U + Mean 50.02

relative error 150 v Mean U + Mean / - 0.0004

Project remarks . . .

Example 2 is simply demonstrative of the Histogram.

It would be a non sense to measure 100 times the same experiment.

Some advocate only 3 repeated measurement for same target value.

That makes sense on the account that measurements are scanned

thus compatible to exponential smoothing of the input.

This is particularly true considering the speed of data acquisition.

Inspect the relative errors . . .

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v v 4752 range 11 range el :

v Mean 50.03

MCD 0.00418 v incertitude 0.14

U v incertitude ± : 0.14 0.14 - 21 sys

v Mean U + 50.17 49.89 21 sys

v Mean U + Mean 50.03

relative error 150 v Mean U + Mean / - 0.0006